Nonlinear multivariate tests for high-dimensional data using wavelets with applications in genomics and engineering

[1]  Ronald R. Coifman,et al.  Entropy-based algorithms for best basis selection , 1992, IEEE Trans. Inf. Theory.

[2]  Thomas G. Dietterich,et al.  Solving Multiclass Learning Problems via Error-Correcting Output Codes , 1994, J. Artif. Intell. Res..

[3]  Franck Picard,et al.  Author's Personal Copy Computational Statistics and Data Analysis Joint Segmentation of Multivariate Gaussian Processes Using Mixed Linear Models , 2022 .

[4]  James O. Ramsay,et al.  Applied Functional Data Analysis: Methods and Case Studies , 2002 .

[5]  Milos Doroslovacki,et al.  On the least asymmetric wavelets , 1998, IEEE Trans. Signal Process..

[6]  E. Lehmann.  Testing Statistical Hypotheses , 1960 .

[7]  Brani Vidakovic,et al.  Wavelet Functional ANOVA, Bayesian False Discovery Rate, and Longitudinal Measurements of Oxygen Pressure in Rats , 2000 .

[8]  Eric Chicken,et al.  Block-dependent thresholding in wavelet regression , 2005 .

[9]  Murray K. Clayton,et al.  An application of Bayesian variable selection to spatial concurrent linear models , 2012, Environmental and Ecological Statistics.

[10]  Peter Guttorp,et al.  Long-Memory Processes, the Allan Variance and Wavelets , 1994 .

[11]  M. Nachman,et al.  Single nucleotide polymorphisms and recombination rate in humans. , 2001, Trends in genetics : TIG.

[12]  William Amos,et al.  Heterogeneous distribution of SNPs in the human genome: microsatellites as predictors of nucleotide diversity and divergence. , 2010, Genomics.

[13]  A. Walden,et al.  Wavelet Methods for Time Series Analysis , 2000 .

[14]  Gerda Claeskens,et al.  Variable selection in partially linear wavelet models , 2011 .

[15]  T. Fearn,et al.  Bayesian Wavelet Regression on Curves With Application to a Spectroscopic Calibration Problem , 2001 .

[16]  J. Tukey,et al.  Transformations Related to the Angular and the Square Root , 1950 .

[17]  James O. Ramsay,et al.  Functional Components of Variation in Handwriting , 2000 .

[18]  B. Vidakovic.  Nonlinear wavelet shrinkage with Bayes rules and Bayes factors , 1998 .

[19]  B. Silverman,et al.  Functional Data Analysis , 1997 .

[20]  S. S. Wilks.  The Large-Sample Distribution of the Likelihood Ratio for Testing Composite Hypotheses , 1938 .

[21]  Donald B. Percival,et al.  Asymptotic decorrelation of between-Scale Wavelet coefficients , 2005, IEEE Transactions on Information Theory.

[22]  Guy P. Nason,et al.  Wavelet regression by cross-validation, , 1994 .

[23]  C. Chui,et al.  A dual-chain approach for bottom–up construction of wavelet filters with any integer dilation , 2012 .

[24]  J.B. Allen,et al.  A unified approach to short-time Fourier analysis and synthesis , 1977, Proceedings of the IEEE.

[25]  T. Tony Cai,et al.  ON BLOCK THRESHOLDING IN WAVELET REGRESSION: ADAPTIVITY, BLOCK SIZE, AND THRESHOLD LEVEL , 2002 .

[26]  Anestis Antoniadis,et al.  Wavelet regression for random or irregular design , 1998 .

[27]  R. Duffin,et al.  A class of nonharmonic Fourier series , 1952 .

[28]  K. Zou,et al.  Receiver-Operating Characteristic Analysis for Evaluating Diagnostic Tests and Predictive Models , 2007, Circulation.

[29]  William Stafford Noble,et al.  Unsupervised segmentation of continuous genomic data , 2007, Bioinform..

[30]  S. Mallat.  A wavelet tour of signal processing , 1998 .

[31]  R. Ogden,et al.  Essential Wavelets for Statistical Applications and Data Analysis , 1996 .

[32]  Di Chen,et al.  Wavelet-Based Data Reduction Techniques for Process Fault Detection , 2006, Technometrics.

[33]  Ronald A. Cole,et al.  Spoken Letter Recognition , 1990, HLT.

[34]  W. Scott Spangler,et al.  Class visualization of high-dimensional data with applications , 2002, Comput. Stat. Data Anal..

[35]  William Stafford Noble,et al.  The spring-loaded genome: Nucleosome redistributions are widespread, transient, and DNA-directed , 2014, Genome research.

[36]  M. Wigler,et al.  Circular binary segmentation for the analysis of array-based DNA copy number data. , 2004, Biostatistics.

[37]  J. Tukey,et al.  An algorithm for the machine calculation of complex Fourier series , 1965 .

[38]  R Core Team,et al.  R: A language and environment for statistical computing. , 2014 .

[39]  B. Mallick,et al.  Functional clustering by Bayesian wavelet methods , 2006 .

[40]  Aaron F. Bobick,et al.  Multiscale 3-D Shape Representation and Segmentation Using Spherical Wavelets , 2007, IEEE Transactions on Medical Imaging.

[41]  G. Weiss,et al.  Littlewood-Paley Theory and the Study of Function Spaces , 1991 .

[42]  Minh N. Do,et al.  Wavelet-based texture retrieval using generalized Gaussian density and Kullback-Leibler distance , 2002, IEEE Trans. Image Process..

[43]  Jionghua Jin,et al.  Feature-preserving data compression of stamping tonnage information using wavelets , 1999 .

[44]  T. Cai,et al.  Block thresholding for density estimation: local and global adaptivity , 2005 .

[45]  Bernadette Govaerts,et al.  Analysing the Results of a Designed Experiment when the Response is a Curve: Methodology and Application in Metal Injection Moulding , 2005 .

[46]  Satterthwaite Fe.  An approximate distribution of estimates of variance components. , 1946 .

[47]  Pierre Baldi,et al.  A Bayesian framework for the analysis of microarray expression data: regularized t -test and statistical inferences of gene changes , 2001, Bioinform..

[48]  Editors-in-chief,et al.  Encyclopedia of statistics in behavioral science , 2005 .

[49]  Bruce I. Turetsky,et al.  Wavelet ANOVA and fMRI , 1999, Optics & Photonics.

[50]  Daniel Boley,et al.  Using Low-Memory Representations to Cluster Very Large Data Sets , 2003, SDM.

[51]  Samuel Kaski,et al.  Discriminative components of data , 2005, IEEE Transactions on Neural Networks.

[52]  A. Bird,et al.  Epigenetic regulation of gene expression: how the genome integrates intrinsic and environmental signals , 2003, Nature Genetics.

[53]  Yoram Singer,et al.  Reducing Multiclass to Binary: A Unifying Approach for Margin Classifiers , 2000, J. Mach. Learn. Res..

[54]  L D Cromwell,et al.  Filtering noise from images with wavelet transforms , 1991, Magnetic resonance in medicine.

[55]  I. Johnstone,et al.  Adapting to Unknown Smoothness via Wavelet Shrinkage , 1995 .

[56]  G. Lorden.  PROCEDURES FOR REACTING TO A CHANGE IN DISTRIBUTION , 1971 .

[57]  Stéphane Mallat,et al.  Multifrequency channel decompositions of images and wavelet models , 1989, IEEE Trans. Acoust. Speech Signal Process..

[58]  Wolfgang Dahmen,et al.  Wavelets on Manifolds I: Construction and Domain Decomposition , 1999, SIAM J. Math. Anal..

[59]  Jye-Chyi Lu,et al.  Wavelet-based SPC procedure for complicated functional data , 2006 .

[60]  Zixiang Xiong,et al.  Wavelet Image Compression , 2009 .

[61]  Hypothesis Testing in a Fractional Ornstein-Uhlenbeck Model , 2012 .

[62]  Michèle Basseville,et al.  Detection of abrupt changes: theory and application , 1993 .

[63]  Patrick Flandrin,et al.  Wavelet analysis and synthesis of fractional Brownian motion , 1992, IEEE Trans. Inf. Theory.

[64]  Hong-Ye Gao,et al.  Wavelet Shrinkage Denoising Using the Non-Negative Garrote , 1998 .

[65]  M. Clyde,et al.  Multiple shrinkage and subset selection in wavelets , 1998 .

[66]  E. S. Pearson,et al.  On the Problem of the Most Efficient Tests of Statistical Hypotheses , 1933 .

[67]  K. Moder.  How to keep the Type I Error Rate in ANOVA if Variances are Heteroscedastic , 2016 .

[68]  H. Hotelling,et al.  Multivariate Quality Control , 1947 .

[69]  Almaz Butaev,et al.  On continuous wavelet transforms of distributions , 2011, Appl. Math. Lett..

[70]  A. Tamhane,et al.  Multiple Comparison Procedures , 1989 .

[71]  Oldrich A. Vasicek.  An equilibrium characterization of the term structure , 1977 .

[72]  G. Nason.  Wavelet Shrinkage using Cross-validation , 1996 .

[73]  R. Redon,et al.  Copy Number Variation: New Insights in Genome Diversity References , 2006 .

[74]  Douglas M. Hawkins,et al.  A variance-stabilizing transformation for gene-expression microarray data , 2002, ISMB.

[75]  T. Gasser,et al.  Statistical Tools to Analyze Data Representing a Sample of Curves , 1992 .

[76]  W. W. Daniel.  Applied Nonparametric Statistics , 1979 .

[77]  Welch Bl.  THE GENERALIZATION OF ‘STUDENT'S’ PROBLEM WHEN SEVERAL DIFFERENT POPULATION VARLANCES ARE INVOLVED , 1947 .

[78]  S. Schuster.  Next-generation sequencing transforms today's biology , 2008, Nature Methods.

[79]  Jin-Ting Zhang,et al.  One‐Way anova for Functional Data via Globalizing the Pointwise F‐test , 2014 .

[80]  E. L. Lehmann,et al.  “Student” and small-sample theory , 1999 .

[81]  Y. Benjamini,et al.  Controlling the false discovery rate: a practical and powerful approach to multiple testing , 1995 .

[82]  J. Daudin,et al.  A Segmentation/Clustering Model for the Analysis of Array CGH Data , 2007, Biometrics.

[83]  Alex Smola,et al.  Kernel methods in machine learning , 2007, math/0701907.

[84]  I. Johnstone,et al.  Threshold selection for wavelet shrinkage of noisy data , 1994, Proceedings of 16th Annual International Conference of the IEEE Engineering in Medicine and Biology Society.

[85]  Stéphane Mallat,et al.  A Theory for Multiresolution Signal Decomposition: The Wavelet Representation , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[86]  H. Chipman,et al.  Adaptive Bayesian Wavelet Shrinkage , 1997 .

[87]  I. Johnstone,et al.  Ideal spatial adaptation by wavelet shrinkage , 1994 .

[88]  T. W. Anderson.  An Introduction to Multivariate Statistical Analysis , 1959 .

[89]  Ricardo Fraiman,et al.  An anova test for functional data , 2004, Comput. Stat. Data Anal..

[90]  I. Johnstone,et al.  Minimax estimation via wavelet shrinkage , 1998 .

[91]  D. Pinkel,et al.  Comparative Genomic Hybridization for Molecular Cytogenetic Analysis of Solid Tumors , 2022 .

[92]  M. Bartlett.  The Square Root Transformation in Analysis of Variance , 1936 .

[93]  Gilbert Strang,et al.  Wavelets and Dilation Equations: A Brief Introduction , 1989, SIAM Rev..

[94]  Shing I. Chang,et al.  Computer Vision Based Non-contact Surface Roughness Assessment Using Wavelet Transform and Response Surface Methodology , 2005 .

[95]  Ajay N. Jain,et al.  Assembly of microarrays for genome-wide measurement of DNA copy number , 2001, Nature Genetics.

[96]  S. Chib,et al.  Understanding the Metropolis-Hastings Algorithm , 1995 .

[97]  O. Rioul,et al.  Wavelets and signal processing , 1991, IEEE Signal Processing Magazine.

[98]  David L. Donoho,et al.  De-noising by soft-thresholding , 1995, IEEE Trans. Inf. Theory.

[99]  Nasser M. Nasrabadi,et al.  Pattern Recognition and Machine Learning , 2006, Technometrics.

[100]  E. S. Pearson,et al.  ON THE USE AND INTERPRETATION OF CERTAIN TEST CRITERIA FOR PURPOSES OF STATISTICAL INFERENCE PART I , 1928 .

[101]  H. Hotelling.  The Generalization of Student’s Ratio , 1931 .

[102]  D. Kell,et al.  Variable selection in wavelet regression models , 1998 .

[103]  Elisa Rossi,et al.  Epidermal growth factor receptor gene and protein and gefitinib sensitivity in non-small-cell lung cancer. , 2005, Journal of the National Cancer Institute.

[104]  Hanne Larsen,et al.  Analysing multivariate data from designed experiments: a case study of photo‐oxidation in sour cream , 2007, Qual. Reliab. Eng. Int..

[105]  G. Passariello,et al.  Bayesian hierarchical model with wavelet transform coefficients of the ECG in obstructive sleep apnea screening , 2000, Computers in Cardiology 2000. Vol.27 (Cat. 00CH37163).

[106]  Richard A. Johnson,et al.  Applied Multivariate Statistical Analysis , 1983 .

[107]  F. J. Anscombe,et al.  THE TRANSFORMATION OF POISSON, BINOMIAL AND NEGATIVE-BINOMIAL DATA , 1948 .