Robust Statistics for Signal Processing

K-distribution, 103, 121–123 M-estimator, 1, 5, 10–12, 19, 21, 23, 27, 46, 48, 53, 54, 61–63, 67, 100, 110–113, 117, 118, 120, 121, 140, 141, 157, 162, 167, 183, 197, 206, 214, 229, 249, 260 ARMA model, 196 Huber’s, 11, 12, 14, 16, 17, 22, 23, 26, 27, 50, 51, 53, 54, 68, 71, 92, 114–116, 121, 157, 167, 183, 259 linear regression, 54 linear regression model, 49 location, 12, 22 monotone, 11, 12, 17, 71 redescending, 10–12, 71 scale, 10, 13 scatter matrix, 110 scatter matrix (regularized), 118 Tukey’s, 11, 12, 14, 16, 17, 34, 49–51, 71, 157, 167, 259 Tyler’s, 116, 117, 121, 123, 141 Tyler’s regularized, 119 MM-estimator, 64, 67, 100, 198, 199, 214, 240, 242, 249, 251, 252 ARMA model, 198 linear regression model, 67 S-estimator, 64, 66, 71, 197–199, 211, 214, 249, 252, 259 ARMA model, 197 linear regression model, 66 α-stable distribution, 136, 144 α-trimmed mean, 19, 21, 26 l1-loss, 36, 50, 97 τ -estimator, 64, 66, 67, 205, 206, 259, 268 ARMA model, 198 ε-contamination model, 20, 25, 26, 50, 166, 174, 181, 242 ε-neighborhood, 21, 26

[1]  F. Österreicher,et al.  On the construction of least favourable pairs of distributions , 1978 .

[2]  Elvezio Ronchetti,et al.  Robustness Aspects of Model Choice , 1997 .

[3]  Yu. V. Prokhorov.  Convergence of Random Processes and Limit Theorems in Probability Theory , 1956 .

[4]  F. Hampel.  The Influence Curve and Its Role in Robust Estimation , 1974 .

[5]  Are Hjørungnes,et al.  Complex-Valued Matrix Differentiation: Techniques and Key Results , 2007, IEEE Transactions on Signal Processing.

[6]  Louis L. Scharf,et al.  Matched subspace detectors , 1994, IEEE Trans. Signal Process..

[7]  S. Stigler.  Simon Newcomb, Percy Daniell, and the History of Robust Estimation 1885–1920 , 1972 .

[8]  Michael Muma,et al.  An online approach for intracranial pressure forecasting based on signal decomposition and robust statistics , 2013, 2013 IEEE International Conference on Acoustics, Speech and Signal Processing.

[9]  D. Hunter,et al.  A Tutorial on MM Algorithms , 2004 .

[10]  Chih-Ling Tsai,et al.  Outlier Detections in Autoregressive Models , 2003 .

[11]  Hannu Oja,et al.  The affine equivariant sign covariance matrix: asymptotic behavior and efficiencies , 2003 .

[12]  C. Hurvich,et al.  High Breakdown Methods of Time Series Analysis , 1993 .

[13]  Abdelhak M. Zoubir,et al.  Multiuser Detection in Heavy Tailed Noise , 2002, Digit. Signal Process..

[14]  Igor Djurovic,et al.  Robust L-estimation based forms of signal transforms and time-frequency representations , 2003, IEEE Trans. Signal Process..

[15]  P. Tseng.  Convergence of a Block Coordinate Descent Method for Nondifferentiable Minimization , 2001 .

[16]  Brian M. Sadler,et al.  On some detection and estimation problems in heavy-tailed noise , 2002, Signal Process..

[17]  Prabhu Babu,et al.  Regularized Tyler's Scatter Estimator: Existence, Uniqueness, and Algorithms , 2014, IEEE Transactions on Signal Processing.

[18]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[19]  Visa Koivunen,et al.  DoA Estimation Via Manifold Separation for Arbitrary Array Structures , 2007, IEEE Transactions on Signal Processing.

[20]  B. Efron.  Bootstrap Methods: Another Look at the Jackknife , 1979 .

[21]  F. Gustafsson,et al.  Mobile positioning using wireless networks: possibilities and fundamental limitations based on available wireless network measurements , 2005, IEEE Signal Processing Magazine.

[22]  Sonja Kuhnt,et al.  Robustness and Complex Data Structures , 2013 .

[23]  H. Vincent Poor,et al.  Complex-valued signal processing — essential models, tools and statistics , 2011, 2011 Information Theory and Applications Workshop.

[24]  Abdelhak M. Zoubir,et al.  A Linear Programming Approach to Sequential Hypothesis Testing , 2015, 1501.05870.

[25]  Ulrich Hammes,et al.  Transformation-Based Robust Semiparametric Estimation , 2008, IEEE Signal Processing Letters.

[26]  Christophe Croux,et al.  Robust and Sparse Factor Modelling , 2011 .

[27]  Rory A. Fisher,et al.  Theory of Statistical Estimation , 1925, Mathematical Proceedings of the Cambridge Philosophical Society.

[28]  Matthew R. McKay,et al.  Large dimensional analysis and optimization of robust shrinkage covariance matrix estimators , 2014, J. Multivar. Anal..

[29]  Boualem Boashash,et al.  The bootstrap and its application in signal processing , 1998, IEEE Signal Process. Mag..

[30]  Malene Højbjerre,et al.  Lecture Notes in Statistics 101: Linear and Graphical Models for the Multivariate Complex Normal Distribution , 1995 .

[31]  David E. Tyler,et al.  On the uniqueness of S-functionals and M-functionals under nonelliptical distributions , 2000 .

[32]  S. Arridge,et al.  Detection and modeling of non‐Gaussian apparent diffusion coefficient profiles in human brain data , 2002, Magnetic resonance in medicine.

[33]  C. Masreliez.  Approximate non-Gaussian filtering with linear state and observation relations , 1975 .

[34]  David E. Tyler.  A Distribution-Free $M$-Estimator of Multivariate Scatter , 1987 .

[35]  L. Scharf,et al.  Statistical Signal Processing of Complex-Valued Data: The Theory of Improper and Noncircular Signals , 2010 .

[36]  Michael Muma,et al.  Computationally efficient algorithm for photoplethysmography-based atrial fibrillation detection using smartphones , 2017, 2017 39th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC).

[37]  J. Astola,et al.  Vector median filters , 1990, Proc. IEEE.

[38]  H. Vincent Poor,et al.  Complex Elliptically Symmetric Distributions: Survey, New Results and Applications , 2012, IEEE Transactions on Signal Processing.

[39]  R. Tibshirani,et al.  PATHWISE COORDINATE OPTIMIZATION , 2007, 0708.1485.

[40]  Rudolf Dutter,et al.  Robust time series analysis: a survey , 1987, Kybernetika.

[41]  Abdefihak M. Zoubir,et al.  Bootstrap Methods and Applications , 2007, IEEE Signal Processing Magazine.

[42]  Roland Fried,et al.  Robust estimation of (partial) autocorrelation , 2015 .

[43]  Preben E. Mogensen,et al.  A stochastic model of the temporal and azimuthal dispersion seen at the base station in outdoor propagation environments , 2000, IEEE Trans. Veh. Technol..

[44]  S. Kotz,et al.  Symmetric Multivariate and Related Distributions , 1989 .

[45]  V. Yohai,et al.  Robust Estimation for ARMA models , 2009, 0904.0106.

[46]  Werner A. Stahel,et al.  Robust Statistics: The Approach Based on Influence Functions , 1987 .

[47]  Ami Wiesel,et al.  Automatic diagonal loading for Tyler's robust covariance estimator , 2016, 2016 IEEE Statistical Signal Processing Workshop (SSP).

[48]  Zhi-Quan Luo,et al.  Robust adaptive beamforming using worst-case performance optimization: a solution to the signal mismatch problem , 2003, IEEE Trans. Signal Process..

[49]  G. Schwarz.  Estimating the Dimension of a Model , 1978 .

[50]  H. Theil.  A Rank-Invariant Method of Linear and Polynomial Regression Analysis , 1992 .

[51]  Visa Koivunen.  Nonlinear filtering of multivariate images under robust error criterion , 1996, IEEE Trans. Image Process..

[52]  Trevor Hastie,et al.  Statistical Learning with Sparsity: The Lasso and Generalizations , 2015 .

[53]  Marius Pesavento,et al.  Direction finding in partly calibrated sensor arrays composed of multiple subarrays , 2002, IEEE Trans. Signal Process..

[54]  H. Zou.  The Adaptive Lasso and Its Oracle Properties , 2006 .

[55]  James A. Reeds,et al.  Asymptotic Number of Roots of Cauchy Location Likelihood Equations , 1985 .

[56]  D. B. Preston.  Spectral Analysis and Time Series , 1983 .

[57]  D. Koller,et al.  Population genomics of human gene expression , 2007, Nature Genetics.

[58]  M. Viberg,et al.  Two decades of array signal processing research: the parametric approach , 1996, IEEE Signal Process. Mag..

[59]  S. Drake,et al.  Dialogue concerning the Two Chief World Systems , 1954 .

[60]  Peter J. Rousseeuw,et al.  ROBUST REGRESSION BY MEANS OF S-ESTIMATORS , 1984 .

[61]  Visa Koivunen,et al.  Recursive Householder-based Space-time Processor for Jammer Mitigation in Navigation Receivers , 2004 .

[62]  Peter J. Rousseeuw,et al.  Robust regression and outlier detection , 1987 .

[63]  Esa Ollila,et al.  Single-snapshot DoA estimation using adaptive elastic net in the complex domain , 2016, 2016 4th International Workshop on Compressed Sensing Theory and its Applications to Radar, Sonar and Remote Sensing (CoSeRa).

[64]  Athina P. Petropulu,et al.  Data traffic modeling—A signal processing perspective , 2003 .

[65]  P Drouin,et al.  Self-monitoring of blood glucose significantly improves metabolic control in patients with type 2 diabetes mellitus: the Auto-Surveillance Intervention Active (ASIA) study. , 2003, Diabetes & metabolism.

[66]  Ulrich Hammes,et al.  Robust MT Tracking Based on M-Estimation and Interacting Multiple Model Algorithm , 2011, IEEE Transactions on Signal Processing.

[67]  Hamid Louni.  Outlier Detection in Arma Models , 2008 .

[68]  Ana M. Pires,et al.  ROBUST BOOTSTRAP : AN ALTERNATIVE TO BOOTSTRAPPING ROBUST ESTIMATORS , 2014 .

[69]  David Middleton,et al.  Non-Gaussian Noise Models in Signal Processing for Telecommunications: New Methods and Results for Class A and Class B Noise Models , 1999, IEEE Trans. Inf. Theory.

[70]  R. E. Kalman,et al.  A New Approach to Linear Filtering and Prediction Problems , 2002 .

[71]  Brian M. Sadler,et al.  Maximum-likelihood array processing in non-Gaussian noise with Gaussian mixtures , 2000, IEEE Trans. Signal Process..

[72]  K. Lange,et al.  Coordinate descent algorithms for lasso penalized regression , 2008, 0803.3876.

[73]  Andrzej Cichocki,et al.  Tensor Decompositions for Signal Processing Applications: From two-way to multiway component analysis , 2014, IEEE Signal Processing Magazine.

[74]  V. Yohai,et al.  Influence Functionals for Time Series , 1986 .

[75]  P. Filzmoser,et al.  Algorithms for Projection-Pursuit Robust Principal Component Analysis , 2007 .

[76]  Kesar Singh,et al.  Breakdown theory for bootstrap quantiles , 1998 .

[77]  Pascal Bondon,et al.  Robust estimation of SARIMA models: Application to short-term load forecasting , 2009, 2009 IEEE/SP 15th Workshop on Statistical Signal Processing.

[78]  Eric C. Chi,et al.  Making Tensor Factorizations Robust to Non-Gaussian Noise , 2010, 1010.3043.

[79]  Visa Koivunen,et al.  Subspace-based direction-of-arrival estimation using nonparametric statistics , 2001, IEEE Trans. Signal Process..

[80]  Prabhu Babu,et al.  Majorization-Minimization Algorithms in Signal Processing, Communications, and Machine Learning , 2017, IEEE Transactions on Signal Processing.

[81]  Giuseppe Ricci,et al.  Recursive estimation of the covariance matrix of a compound-Gaussian process and its application to adaptive CFAR detection , 2002, IEEE Trans. Signal Process..

[82]  Björn E. Ottersten,et al.  Weighted subspace fitting for general array error models , 1998, IEEE Trans. Signal Process..

[83]  John W. Tukey,et al.  Exploratory Data Analysis. , 1979 .

[84]  R. Tibshirani.  Regression Shrinkage and Selection via the Lasso , 1996 .

[85]  Visa Koivunen,et al.  Propagation parameter estimation in MIMO systems using mixture of angular distributions model , 2005, Proceedings. (ICASSP '05). IEEE International Conference on Acoustics, Speech, and Signal Processing, 2005..

[86]  Visa Koivunen,et al.  Robust and sparse estimation of tensor decompositions , 2013, 2013 IEEE Global Conference on Signal and Information Processing.

[87]  Yingbo Hua,et al.  High-Resolution and Robust Signal Processing , 2003 .

[88]  V. Yohai,et al.  High Breakdown-Point Estimates of Regression by Means of the Minimization of an Efficient Scale , 1988 .

[89]  Michael Fauß.  Design and Analysis of Optimal and Minimax Robust Sequential Hypothesis Tests , 2016 .

[90]  H. Künsch.  Infinitesimal Robustness for Autoregressive Processes , 1984 .

[91]  Louis L. Scharf,et al.  Adaptive subspace detectors , 2001, IEEE Trans. Signal Process..

[92]  Xiaoli Gao,et al.  Asymptotic analysis of high-dimensional LAD regression with Lasso , 2016 .

[93]  Esa Ollila.  Optimal high-dimensional shrinkage covariance estimation for elliptical distributions , 2017, 2017 25th European Signal Processing Conference (EUSIPCO).

[94]  Lamine Mili,et al.  A Robust GM-Estimator for the Automated Detection of External Defects on Barked Hardwood Logs and Stems , 2007, IEEE Transactions on Signal Processing.

[95]  Visa Koivunen,et al.  Robust, Scalable, and Fast Bootstrap Method for Analyzing Large Scale Data , 2016, IEEE Transactions on Signal Processing.

[96]  Jian Li,et al.  On robust Capon beamforming and diagonal loading , 2003, IEEE Trans. Signal Process..

[97]  Esa Ollila,et al.  Multichannel sparse recovery of complex-valued signals using Huber's criterion , 2015, 2015 3rd International Workshop on Compressed Sensing Theory and its Applications to Radar, Sonar and Remote Sensing (CoSeRa).

[98]  Abdelhak M. Zoubir,et al.  Minimax Robust Hypothesis Testing , 2015, IEEE Transactions on Information Theory.

[99]  Danilo P. Mandic,et al.  Complex Valued Nonlinear Adaptive Filters , 2009 .

[100]  Ta-Hsin Li.  A Nonlinear Method for Robust Spectral Analysis , 2010, IEEE Transactions on Signal Processing.

[101]  B. A. D. H. Brandwood.  A complex gradient operator and its applica-tion in adaptive array theory , 1983 .

[102]  L. Rudin,et al.  Nonlinear total variation based noise removal algorithms , 1992 .

[103]  J. Friedman,et al.  A Statistical View of Some Chemometrics Regression Tools , 1993 .

[104]  Willis J. Tompkins,et al.  A Real-Time QRS Detection Algorithm , 1985, IEEE Transactions on Biomedical Engineering.

[105]  Olivier Ledoit,et al.  A well-conditioned estimator for large-dimensional covariance matrices , 2004 .

[106]  Abdelhak M. Zoubir,et al.  Measuring Blood Glucose Concentrations in Photometric Glucometers Requiring Very Small Sample Volumes , 2016, IEEE Transactions on Biomedical Engineering.

[107]  David E. Tyler,et al.  Redescending $M$-Estimates of Multivariate Location and Scatter , 1991 .

[108]  B. G. Quinn,et al.  The determination of the order of an autoregression , 1979 .

[109]  Visa Koivunen,et al.  Complex Elliptically Symmetric Random Variables—Generation, Characterization, and Circularity Tests , 2011, IEEE Transactions on Signal Processing.

[110]  Michael Muma,et al.  A new method for heart rate monitoring during physical exercise using photoplethysmographic signals , 2015, 2015 23rd European Signal Processing Conference (EUSIPCO).

[111]  Ming Ye,et al.  Estimating Piecewise-Smooth Optical Flow with Global Matching and Graduated Optimization , 2003, IEEE Trans. Pattern Anal. Mach. Intell..

[112]  Gonzalo R. Arce,et al.  Optimality of the myriad filter in practical impulsive-noise environments , 2001, IEEE Trans. Signal Process..

[113]  Abdelhak M. Zoubir,et al.  Bootstrap techniques for signal processing , 2004 .

[114]  Ioannis Pitas,et al.  Nonlinear Digital Filters - Principles and Applications , 1990, The Springer International Series in Engineering and Computer Science.

[115]  Zhi-Quan Luo,et al.  A Unified Convergence Analysis of Block Successive Minimization Methods for Nonsmooth Optimization , 2012, SIAM J. Optim..

[116]  H. Vincent Poor,et al.  Robust multiuser detection in non-Gaussian channels , 1999, IEEE Trans. Signal Process..

[117]  B. Carlson.  Covariance matrix estimation errors and diagonal loading in adaptive arrays , 1988 .

[118]  Michael Muma,et al.  Robustness Analysis of Spatial Time-Frequency Distributions Based on the Influence Function , 2013, IEEE Transactions on Signal Processing.

[119]  Philippe Forster,et al.  Covariance Structure Maximum-Likelihood Estimates in Compound Gaussian Noise: Existence and Algorithm Analysis , 2008, IEEE Transactions on Signal Processing.

[120]  P. Rousseeuw.  Multivariate estimation with high breakdown point , 1985 .

[121]  V. Koivunen,et al.  Householder Multistage Wiener Filter for Space-Time Navigation Receivers , 2007, IEEE Transactions on Aerospace and Electronic Systems.

[122]  Cun-Hui Zhang,et al.  The multivariate L1-median and associated data depth. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[123]  Alfred O. Hero,et al.  Shrinkage Algorithms for MMSE Covariance Estimation , 2009, IEEE Transactions on Signal Processing.

[124]  Iickho Song,et al.  Advanced Theory of Signal Detection: Weak Signal Detection in Generalized Observations , 2010 .

[125]  R. Tsay.  Outliers, Level Shifts, and Variance Changes in Time Series , 1988 .

[126]  P. J. Huber.  The 1972 Wald Lecture Robust Statistics: A Review , 1972 .

[127]  S. Mitter,et al.  Robust Recursive Estimation in the Presence of Heavy-Tailed Observation Noise , 1994 .

[128]  Visa Koivunen,et al.  Application of Manifold Separation to Polarimetric Capon Beamformer and Source Tracking , 2014, IEEE Transactions on Signal Processing.

[129]  Mia Hubert,et al.  Robust PARAFAC for incomplete data , 2012 .

[130]  V. Yohai.  HIGH BREAKDOWN-POINT AND HIGH EFFICIENCY ROBUST ESTIMATES FOR REGRESSION , 1987 .

[131]  M. Shirosaki.  Another proof of the defect relation for moving targets , 1991 .

[132]  G. Ljung,et al.  On Outlier Detection in Time Series , 1993 .

[133]  Michael Muma,et al.  Robust Estimation in Signal Processing: A Tutorial-Style Treatment of Fundamental Concepts , 2012, IEEE Signal Processing Magazine.

[134]  Yuri I. Abramovich,et al.  Diagonally Loaded Normalised Sample Matrix Inversion (LNSMI) for Outlier-Resistant Adaptive Filtering , 2007, 2007 IEEE International Conference on Acoustics, Speech and Signal Processing - ICASSP '07.

[135]  Louis A. Jaeckel.  Estimating Regression Coefficients by Minimizing the Dispersion of the Residuals , 1972 .

[136]  Yacine Chitour,et al.  Generalized Robust Shrinkage Estimator and Its Application to STAP Detection Problem , 2013, IEEE Transactions on Signal Processing.

[137]  Conceição Amado,et al.  Robust Bootstrap with Non Random Weights Based on the Influence Function , 2004 .

[138]  Alfred O. Hero,et al.  Robust Shrinkage Estimation of High-Dimensional Covariance Matrices , 2010, IEEE Transactions on Signal Processing.

[139]  Robust Akaike Information Criterion for ARMA models , 2004 .

[140]  Yacine Chakhchoukh,et al.  A New Robust Estimation Method for ARMA Models , 2009, IEEE Transactions on Signal Processing.

[141]  Michael Muma,et al.  Bounded Influence Propagation $\tau$ -Estimation: A New Robust Method for ARMA Model Estimation , 2016, IEEE Transactions on Signal Processing.

[142]  Ulrich Richard Hammes,et al.  Robust Positioning Algorithms for Wireless Networks , 2010 .

[143]  E. Lehmann,et al.  Nonparametrics: Statistical Methods Based on Ranks , 1976 .

[144]  Michael Muma,et al.  Motion artifact removal in ECG signals using multi-resolution thresholding , 2012, 2012 Proceedings of the 20th European Signal Processing Conference (EUSIPCO).

[145]  Hansheng Wang,et al.  Robust Regression Shrinkage and Consistent Variable Selection Through the LAD-Lasso , 2007 .

[146]  Huijun Gao,et al.  Robust $H_{\infty}$ Filtering for a Class of Nonlinear Networked Systems With Multiple Stochastic Communication Delays and Packet Dropouts , 2010, IEEE Transactions on Signal Processing.

[147]  L.L. Scharf,et al.  Adaptive matched subspace detectors and adaptive coherence estimators , 1996, Conference Record of The Thirtieth Asilomar Conference on Signals, Systems and Computers.

[148]  B. Andrews,et al.  Rank‐based estimation for autoregressive moving average time series models , 2007 .

[149]  E.J. Candes,et al.  An Introduction To Compressive Sampling , 2008, IEEE Signal Processing Magazine.

[150]  Trevor J. Hastie,et al.  Genome-wide association analysis by lasso penalized logistic regression , 2009, Bioinform..

[151]  P. L. Davies.  Aspects of Robust Linear Regression , 1993 .

[152]  Douglas B. Williams,et al.  Robust estimation of structured covariance matrices , 1993, IEEE Trans. Signal Process..

[153]  Abdelhak M. Zoubir,et al.  Robust Hypothesis Testing with $\alpha $ -Divergence , 2016, IEEE Transactions on Signal Processing.

[154]  Richard G. Baraniuk,et al.  Compressive Sensing , 2008, Computer Vision, A Reference Guide.

[155]  S. Sheather,et al.  Robust Estimation and Testing , 1990 .

[156]  Hannu Oja,et al.  INFLUENCE FUNCTION AND ASYMPTOTIC EFFICIENCY OF THE AFFINE EQUIVARIANT RANK COVARIANCE MATRIX , 2004 .

[157]  Abdelhak M. Zoubir,et al.  Old Bands, New Tracks—Revisiting the Band Model for Robust Hypothesis Testing , 2015, IEEE Transactions on Signal Processing.

[158]  N. R. Goodman.  Statistical analysis based on a certain multivariate complex Gaussian distribution , 1963 .

[159]  Ismail Güvenç,et al.  A Survey on TOA Based Wireless Localization and NLOS Mitigation Techniques , 2009, IEEE Communications Surveys & Tutorials.

[160]  Charles V. Stewart,et al.  Robust Parameter Estimation in Computer Vision , 1999, SIAM Rev..

[161]  Christoph F. Mecklenbräuker,et al.  Multiple and single snapshot compressive beamforming. , 2015, The Journal of the Acoustical Society of America.

[162]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[163]  Esa Ollila,et al.  Regularized $M$ -Estimators of Scatter Matrix , 2014, IEEE Transactions on Signal Processing.

[164]  Kenneth E. Barner,et al.  Meridian Filtering for Robust Signal Processing , 2007, IEEE Transactions on Signal Processing.

[165]  Marc G. Genton,et al.  Comprehensive definitions of breakdown points for independent and dependent observations , 2003 .

[166]  Kaj Madsen,et al.  Methods for Non-Linear Least Squares Problems (2nd ed.) , 2004 .

[167]  Adriaan van den Bos,et al.  The multivariate complex normal distribution-a generalization , 1995, IEEE Trans. Inf. Theory.

[168]  C. Croux.  Limit behavior of the empirical influence function of the median , 1998 .

[169]  D. Mandic,et al.  Complex Valued Nonlinear Adaptive Filters: Noncircularity, Widely Linear and Neural Models , 2009 .

[170]  Bernhard Spangl,et al.  Robust Kalman tracking and smoothing with propagating and non-propagating outliers , 2012, 1204.3358.

[171]  P. L. Davies,et al.  Asymptotic behaviour of S-estimates of multivariate location parameters and dispersion matrices , 1987 .

[172]  Visa Koivunen,et al.  Unified Array Manifold Decomposition Based on Spherical Harmonics and 2-D Fourier Basis , 2010, IEEE Transactions on Signal Processing.

[173]  Trevor Hastie,et al.  The Elements of Statistical Learning , 2001 .

[174]  Abdelhak M. Zoubir,et al.  Robust bootstrap based observation classification for Kalman Filtering in harsh LOS/NLOS environments , 2014, 2014 IEEE Workshop on Statistical Signal Processing (SSP).

[175]  H. Zou,et al.  Regularization and variable selection via the elastic net , 2005 .

[176]  Alexander G. Tartakovsky,et al.  Sequential Analysis: Design Methods and Applications Nearly Minimax One-sided Mixture-based Sequential Tests Nearly Minimax One-sided Mixture-based Sequential Tests , 2022 .

[177]  A. Bos.  Complex gradient and Hessian , 1994 .

[178]  Ami Wiesel,et al.  Performance Analysis of Tyler's Covariance Estimator , 2014, IEEE Transactions on Signal Processing.

[179]  Visa Koivunen,et al.  Statistics for complex random variables revisited , 2009, 2009 IEEE International Conference on Acoustics, Speech and Signal Processing.

[180]  Visa Koivunen,et al.  Sparse regularization of tensor decompositions , 2013, 2013 IEEE International Conference on Acoustics, Speech and Signal Processing.

[181]  P. J. Huber.  Robust Estimation of a Location Parameter , 1964 .

[182]  Stuart Jay Deutsch,et al.  Effects of a single outlier on arma identification , 1990 .

[183]  Antonio Ramón Jiménez,et al.  RoPEUS: A New Robust Algorithm for Static Positioning in Ultrasonic Systems , 2009, Sensors.

[184]  R. T. Hoctor,et al.  The unifying role of the coarray in aperture synthesis for coherent and incoherent imaging , 1990, Proc. IEEE.

[185]  Martin Vetterli,et al.  A robust method for inverse transport modeling of atmospheric emissions using blind outlier detection , 2014 .

[186]  S.A. Kassam,et al.  Robust techniques for signal processing: A survey , 1985, Proceedings of the IEEE.

[187]  Ruben H. Zamar,et al.  The Fast-τ Estimator for Regression , 2008 .

[188]  Abdelhak M. Zoubir,et al.  A robust kernel density estimator based mean-shift algorithm , 2014, 2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[189]  Ami Wiesel,et al.  Structured Robust Covariance Estimation , 2015, Found. Trends Signal Process..

[190]  PETER J. ROUSSEEUW,et al.  Computing LTS Regression for Large Data Sets , 2005, Data Mining and Knowledge Discovery.

[191]  Xuelong Li,et al.  Robust Tensor Analysis With L1-Norm , 2010, IEEE Transactions on Circuits and Systems for Video Technology.

[192]  F. Götze,et al.  RESAMPLING FEWER THAN n OBSERVATIONS: GAINS, LOSSES, AND REMEDIES FOR LOSSES , 2012 .

[193]  Ta-Hsin Li,et al.  Laplace Periodogram for Time Series Analysis , 2008 .

[194]  Visa Koivunen,et al.  Sequential Unfolding SVD for Tensors With Applications in Array Signal Processing , 2009, IEEE Transactions on Signal Processing.

[195]  Lamine Mili,et al.  Robust state estimation of electric power systems , 1994 .

[196]  David E. Tyler,et al.  Simultaneous penalized M-estimation of covariance matrices using geodesically convex optimization , 2016, 1608.08126.

[197]  I. Barrodale,et al.  An Improved Algorithm for Discrete $l_1 $ Linear Approximation , 1973 .

[198]  Chih-Ling Tsai,et al.  A note on the unification of the Akaike information criterion , 1998 .

[199]  Tülay Adali,et al.  Complex-Valued Signal Processing: The Proper Way to Deal With Impropriety , 2011, IEEE Transactions on Signal Processing.

[200]  F. Gini.  Sub-optimum coherent radar detection in a mixture of K-distributed and Gaussian clutter , 1997 .

[201]  F. Hampel.  Contributions to the theory of robust estimation , 1968 .

[202]  A. Lee Swindlehurst,et al.  A Performance Analysis of Subspace-Based Methods in the Presence of Model Errors: Part &-Multidimensional Algorithms , 1993 .

[203]  Nikos D. Sidiropoulos,et al.  Robust iterative fitting of multilinear models , 2005, IEEE Transactions on Signal Processing.

[204]  Theodore S. Rappaport,et al.  Measurements and simulation of radio frequency impulsive noise in hospitals and clinics , 1997, 1997 IEEE 47th Vehicular Technology Conference. Technology in Motion.

[205]  Lamine Mili,et al.  Robust Kalman Filter Based on a Generalized Maximum-Likelihood-Type Estimator , 2010, IEEE Transactions on Signal Processing.

[206]  Michael D. Zoltowski,et al.  Beamspace Root-MUSIC , 1993, IEEE Trans. Signal Process..

[207]  Hannu Oja,et al.  Estimates of Regression Coefficients Based on Lift Rank Covariance Matrix , 2003 .

[208]  Wenjiang J. Fu.  Penalized Regressions: The Bridge versus the Lasso , 1998 .

[209]  P. Rousseeuw,et al.  Breakdown Points of Affine Equivariant Estimators of Multivariate Location and Covariance Matrices , 1991 .

[210]  Esa Ollila.  Adaptive LASSO based on joint M-estimation of regression and scale , 2016, 2016 24th European Signal Processing Conference (EUSIPCO).

[211]  R. Remmert,et al.  Theory of Complex Functions , 1990 .

[212]  Bernard C. Picinbono,et al.  On circularity , 1994, IEEE Trans. Signal Process..

[213]  Ami Wiesel,et al.  Geodesic Convexity and Covariance Estimation , 2012, IEEE Transactions on Signal Processing.

[214]  Michael Muma,et al.  Robust bootstrap methods with an application to geolocation in harsh LOS/NLOS environments , 2014, 2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[215]  Richard H. Jones,et al.  Maximum Likelihood Fitting of ARMA Models to Time Series With Missing Observations , 1980 .

[216]  J. Tamada,et al.  Keeping watch on glucose , 2002 .

[217]  Adrian E. Raftery,et al.  Robust Bayesian Model Selection for Autoregressive Processes with Additive Outliers , 1996 .

[218]  H. Oja,et al.  Sign and rank covariance matrices , 2000 .

[219]  J. Chang,et al.  Analysis of individual differences in multidimensional scaling via an n-way generalization of “Eckart-Young” decomposition , 1970 .

[220]  Louis L. Scharf,et al.  The adaptive coherence estimator: a uniformly most-powerful-invariant adaptive detection statistic , 2005, IEEE Transactions on Signal Processing.

[221]  A. Siegel.  Robust regression using repeated medians , 1982 .

[222]  D. B. Duncan,et al.  Linear Dynamic Recursive Estimation from the Viewpoint of Regression Analysis , 1972 .

[223]  Oscar H. Bustos,et al.  Robust Estimates for ARMA Models , 1986 .

[224]  Korrai Deergha Rao,et al.  A new m-estimator based robust multiuser detection in flat-fading non-gaussian channels , 2009, IEEE Transactions on Communications.

[225]  Visa Koivunen,et al.  New robust LASSO method based on ranks , 2015, 2015 23rd European Signal Processing Conference (EUSIPCO).

[226]  V. Koivunen,et al.  Unitary root-MUSIC technique for uniform circular array , 2003, Proceedings of the 3rd IEEE International Symposium on Signal Processing and Information Technology (IEEE Cat. No.03EX795).

[227]  H. Shahriari,et al.  Parameter Estimation of Autoregressive Models Using the Iteratively Robust Filtered Fast-τ Method , 2014 .

[228]  L. Mili,et al.  Electric Load Forecasting Based on Statistical Robust Methods , 2011, IEEE Transactions on Power Systems.

[229]  Purnamrita Sarkar,et al.  A scalable bootstrap for massive data , 2011, 1112.5016.

[230]  Anthony J. Weiss,et al.  Array shape calibration using sources in unknown locations-a maximum likelihood approach , 1989, IEEE Trans. Acoust. Speech Signal Process..

[231]  Ken Kreutz-Delgado,et al.  The Complex Gradient Operator and the CR-Calculus ECE275A - Lecture Supplement - Fall 2005 , 2009, 0906.4835.

[232]  B. Brodsky,et al.  Minimax Methods for Multihypothesis Sequential Testing and Change-Point Detection Problems , 2008 .

[233]  Gabriel Frahm.  Generalized Elliptical Distributions: Theory and Applications , 2004 .

[234]  Arnold J. Stromberg,et al.  Robust covariance estimates based on resampling , 1997 .

[235]  Esa Ollila,et al.  Distribution-free detection under complex elliptically symmetric clutter distribution , 2012, 2012 IEEE 7th Sensor Array and Multichannel Signal Processing Workshop (SAM).

[236]  R. Martin,et al.  Robust bayesian estimation for the linear model and robustifying the Kalman filter , 1977 .

[237]  Kenneth E. Barner,et al.  Nonlinear Signal and Image Processing: Theory, Methods, and Applications , 2003 .

[238]  David E. Tyler,et al.  Maximum likelihood estimation for the wrapped Cauchy distribution , 1988 .

[239]  Ali H. Sayed,et al.  Robust Adaptation in Impulsive Noise , 2016, IEEE Transactions on Signal Processing.

[240]  A. Zoubir,et al.  A new approach for the quantification of synchrony of multivariate non-stationary psychophysiological variables during emotion eliciting stimuli , 2015, Front. Psychol..

[241]  Abdelhak M. Zoubir,et al.  Mean-shift based algorithm for the measurement of blood glucose in hand-held devices , 2013, 21st European Signal Processing Conference (EUSIPCO 2013).

[242]  M. Roth,et al.  Single‐trial analysis of oddball event‐related potentials in simultaneous EEG‐fMRI , 2007, Human brain mapping.

[243]  S. T. Buckland,et al.  An Introduction to the Bootstrap. , 1994 .

[244]  Esa Ollila,et al.  CONTRIBUTIONS TO INDEPENDENT COMPONENT ANALYSIS, SENSOR ARRAY AND COMPLEX-VALUED SIGNAL PROCESSING , 2010 .

[245]  R. Tibshirani,et al.  Sparsity and smoothness via the fused lasso , 2005 .

[246]  Yong Hoon Lee,et al.  Generalized median filtering and related nonlinear filtering techniques , 1985, IEEE Trans. Acoust. Speech Signal Process..

[247]  Saul Stahl,et al.  The Evolution of the Normal Distribution , 2006 .

[248]  Alfred O. Hero,et al.  Relative location estimation in wireless sensor networks , 2003, IEEE Trans. Signal Process..

[249]  H. Vincent Poor,et al.  Robust iteratively reweighted Lasso for sparse tensor factorizations , 2014, 2014 IEEE Workshop on Statistical Signal Processing (SSP).

[250]  E. Ollila,et al.  Influence functions for array covariance matrix estimators , 2004, IEEE Workshop on Statistical Signal Processing, 2003.

[251]  Saleem A. Kassam,et al.  Robust hypothesis testing for bounded classes of probability densities , 1981, IEEE Trans. Inf. Theory.

[252]  Samuel Müller,et al.  Outlier Robust Model Selection in Linear Regression , 2005 .

[253]  Sergios Theodoridis,et al.  Array and statistical signal processing , 2014 .

[254]  Emmanuel J. Candès,et al.  Near-Optimal Signal Recovery From Random Projections: Universal Encoding Strategies? , 2004, IEEE Transactions on Information Theory.

[255]  Sonja Kuhnt,et al.  Robustness and complex data structures : Festschrift in honour of Ursula Gather , 2013 .

[256]  Victor J. Yohai,et al.  Robust Low-Rank Approximation of Data Matrices With Elementwise Contamination , 2008, Technometrics.

[257]  Gonzalo R. Arce,et al.  A Maximum Likelihood Approach to Least Absolute Deviation Regression , 2004, EURASIP J. Adv. Signal Process..

[258]  Saleem A. Kassam,et al.  A class of nonparametric detectors for dependent input data , 1975, IEEE Trans. Inf. Theory.

[259]  Moncef Gabbouj,et al.  Weighted median filters: a tutorial , 1996 .

[260]  M. H. DeGroot.  Minimax Sequential Tests of Some Composite Hypotheses , 1960 .

[261]  P. J. Huber.  A Robust Version of the Probability Ratio Test , 1965 .

[262]  D. Thomson,et al.  Robust-resistant spectrum estimation , 1982, Proceedings of the IEEE.

[263]  W. M. Carey,et al.  Digital spectral analysis: with applications , 1986 .

[264]  Wing-Kin Ma,et al.  Least squares algorithms for time-of-arrival-based mobile location , 2004, IEEE Transactions on Signal Processing.

[265]  J. Kent.  Data analysis for shapes and images , 1997 .

[266]  V. Koivunen,et al.  Generalized complex elliptical distributions , 2004, Processing Workshop Proceedings, 2004 Sensor Array and Multichannel Signal.

[267]  Stefan Van Aelst,et al.  Fast and robust bootstrap , 2008, Stat. Methods Appl..

[268]  R. Zamar,et al.  Bootstrapping robust estimates of regression , 2002 .

[269]  Esa Ollila,et al.  Direction of arrival estimation using robust complex Lasso , 2016, 2016 10th European Conference on Antennas and Propagation (EuCAP).

[270]  Nikos D. Sidiropoulos,et al.  Tensor Decomposition for Signal Processing and Machine Learning , 2016, IEEE Transactions on Signal Processing.

[271]  Paul C. Etter,et al.  Underwater Acoustic Modeling and Simulation , 2018 .

[272]  Vladimir Katkovnik.  Robust M-periodogram , 1998, IEEE Trans. Signal Process..

[273]  K. Mardia,et al.  Statistical Shape Analysis , 1998 .

[274]  Bernard C. Levy,et al.  Robust Hypothesis Testing With a Relative Entropy Tolerance , 2007, IEEE Transactions on Information Theory.

[275]  P. Krishnaiah,et al.  Complex elliptically symmetric distributions , 1986 .

[276]  Fulvio Gini,et al.  Covariance matrix estimation for CFAR detection in correlated heavy tailed clutter , 2002, Signal Process..

[277]  Visa Koivunen,et al.  Fast and robust bootstrap method for testing hypotheses in the ICA model , 2014, 2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[278]  Tamara G. Kolda,et al.  Tensor Decompositions and Applications , 2009, SIAM Rev..

[279]  Kapil Gulati,et al.  Mitigating near-field interference in laptop embedded wireless transceivers , 2008, ICASSP.

[280]  V. Koivunen,et al.  Robust space-time scatter matrix estimator for broadband antenna arrays , 2003, 2003 IEEE 58th Vehicular Technology Conference. VTC 2003-Fall (IEEE Cat. No.03CH37484).

[281]  Ami Wiesel,et al.  Multivariate Generalized Gaussian Distribution: Convexity and Graphical Models , 2013, IEEE Transactions on Signal Processing.

[282]  R. Koenker.  Quantile Regression: Name Index , 2005 .

[283]  Nikos D. Sidiropoulos,et al.  Co-clustering as multilinear decomposition with sparse latent factors , 2011, 2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[284]  Matthew S. Mayo,et al.  Elemental Subsets: The Building Blocks of Regression , 1997 .

[285]  Michael T. Chryssomallis,et al.  Smart antennas , 2000 .

[286]  Gonzalo R. Arce,et al.  Fast algorithms for weighted myriad computation by fixed-point search , 2000, IEEE Trans. Signal Process..

[287]  Yuri I. Abramovich,et al.  Impulsive Noise Mitigation in Spatial and Temporal Domains for Surface-Wave Over-the-Horizon Radar , 1999 .

[288]  K. Vastola,et al.  Robust Wiener-Kolmogorov theory , 1984, IEEE Trans. Inf. Theory.

[289]  S. Unnikrishna Pillai,et al.  Forward/backward spatial smoothing techniques for coherent signal identification , 1989, IEEE Trans. Acoust. Speech Signal Process..

[290]  Zeljko M. Durovic,et al.  Robust estimation with unknown noise statistics , 1999, IEEE Trans. Autom. Control..

[291]  Kiseon Kim,et al.  Why Gaussianity? , 2008, IEEE Signal Processing Magazine.

[292]  R. Maronna.  Robust $M$-Estimators of Multivariate Location and Scatter , 1976 .

[293]  Abdelhak M. Zoubir.  Chapter 1 - Introduction to Statistical Signal Processing , 2014 .

[294]  G. Box.  NON-NORMALITY AND TESTS ON VARIANCES , 1953 .

[295]  John J. Vaccaro,et al.  Wideband cancellation of interference in a GPS receive array , 2000, IEEE Trans. Aerosp. Electron. Syst..

[296]  Visa Koivunen,et al.  Essential Statistics and Tools for Complex Random Variables , 2010, IEEE Transactions on Signal Processing.

[297]  A. E. Hoerl,et al.  Ridge regression: biased estimation for nonorthogonal problems , 2000 .

[298]  Michael Muma,et al.  Robust model order selection for ARMA models based on the bounded innovation propagation τ-estimator , 2014, 2014 IEEE Workshop on Statistical Signal Processing (SSP).

[299]  Visa Koivunen,et al.  Enhanced bootstrap method for statistical inference in the ICA model , 2017, Signal Process..

[300]  V. Yohai,et al.  A Fast Algorithm for S-Regression Estimates , 2006 .

[301]  G. Box.  Robustness in the Strategy of Scientific Model Building. , 1979 .

[302]  Weize Sun,et al.  ℓp-norm Based Iterative Adaptive Approach for Robust Spectral Analysis , 2014, Signal Process..

[303]  Louis L. Scharf,et al.  A Multistage Representation of the Wiener Filter Based on Orthogonal Projections , 1998, IEEE Trans. Inf. Theory.

[304]  P. Rousseeuw.  Least Median of Squares Regression , 1984 .

[305]  Ulrich Hammes,et al.  Robust Tracking and Geolocation for Wireless Networks in NLOS Environments , 2009, IEEE Journal of Selected Topics in Signal Processing.

[306]  David R. Brillinger,et al.  Time Series: Data Analysis and Theory. , 1982 .

[307]  Richard A. Harshman,et al.  Foundations of the PARAFAC procedure: Models and conditions for an "explanatory" multi-model factor analysis , 1970 .

[308]  V. Yohai,et al.  Robust Statistics: Theory and Methods , 2006 .

[309]  A. Lee Swindlehurst,et al.  A Performance Analysis ofSubspace-Based Methods in thePresence of Model Errors { Part I : The MUSIC AlgorithmA , 1992 .

[310]  M. Genton,et al.  Robust Simulation-Based Estimation of ARMA Models , 2001 .

[311]  P. J. Huber,et al.  Minimax Tests and the Neyman-Pearson Lemma for Capacities , 1973 .

[312]  B. D. Rao,et al.  Performance analysis of subspace based methods (plane wave direction of arrival estimation) , 1988, Fourth Annual ASSP Workshop on Spectrum Estimation and Modeling.

[313]  M. Sion.  On general minimax theorems , 1958 .

[314]  Visa Koivunen,et al.  Robust antenna array processing using M-estimators of pseudo-covariance , 2003, 14th IEEE Proceedings on Personal, Indoor and Mobile Radio Communications, 2003. PIMRC 2003..

[315]  Y. Selen,et al.  Model-order selection: a review of information criterion rules , 2004, IEEE Signal Processing Magazine.