Recent advances in functional data analysis and high-dimensional statistics

This paper provides a structured overview of the contents of this Special Issue of the Journal of Multivariate Analysis devoted to Functional Data Analysis and Related Topics, along with a brief survey of the field.

[1]  Jorge Mateu,et al.  Statistics for spatial functional data: some recent contributions , 2009 .

[2]  Yingxing Li,et al.  Spatial Functional Principal Component Analysis with Applications to Brain Image Data , 2017, J. Multivar. Anal..

[3]  Mustapha Rachdi,et al.  Uniform in bandwidth consistency for various kernel estimators involving functional data , 2017 .

[4]  Denis Bosq,et al.  Estimation of Mean and Covariance Operator of Autoregressive Processes in Banach Spaces , 2002 .

[5]  Stanislav Nagy,et al.  Data depth for measurable noisy random functions , 2019, J. Multivar. Anal..

[6]  R. Fraiman,et al.  Trimmed means for functional data , 2001 .

[7]  Alessandra Menafoglio,et al.  Statistical analysis of complex and spatially dependent data: A review of Object Oriented Spatial Statistics , 2017, Eur. J. Oper. Res..

[8]  Juan Lucas Bali,et al.  Robust estimators under a functional common principal components model , 2017, Computational Statistics & Data Analysis.

[9]  Abdelaziz Allam,et al.  Optimal rate for covariance operator estimators of functional autoregressive processes with random coefficients , 2019, J. Multivar. Anal..

[10]  Ricardo Fraiman,et al.  Connecting pairwise geodesic spheres by depth: DCOPS , 2019, J. Multivar. Anal..

[11]  Taras Bodnar,et al.  Optimal shrinkage estimator for high-dimensional mean vector , 2016, J. Multivar. Anal..

[12]  Fabio Nobile,et al.  Modeling spatially dependent functional data via regression with differential regularization , 2019, J. Multivar. Anal..

[13]  J Steve Marron,et al.  Overview of object oriented data analysis , 2014, Biometrical journal. Biometrische Zeitschrift.

[14]  John A. D. Aston,et al.  Smooth Principal Component Analysis over two-dimensional manifolds with an application to Neuroimaging , 2016, 1601.03670.

[15]  Alain Boudou,et al.  On spectral and random measures associated to discrete and continuous-time processes , 2002 .

[16]  Han Lin Shang,et al.  Methods for Scalar‐on‐Function Regression , 2017, International statistical review = Revue internationale de statistique.

[17]  Joel L. Horowitz,et al.  Methodology and convergence rates for functional linear regression , 2007, 0708.0466.

[18]  Pedro Delicado,et al.  Optimal level sets for bivariate density representation , 2015, J. Multivar. Anal..

[19]  Ricardo Fraiman,et al.  On depth measures and dual statistics. A methodology for dealing with general data , 2009, J. Multivar. Anal..

[20]  Aurore Delaigle,et al.  Componentwise classification and clustering of functional data , 2012 .

[21]  Zhou Yu,et al.  Estimation and testing for partially functional linear errors-in-variables models , 2019, J. Multivar. Anal..

[22]  A. Berlinet,et al.  Reproducing kernel Hilbert spaces in probability and statistics , 2004 .

[23]  Karim Benhenni,et al.  Local polynomial estimation of regression operators from functional data with correlated errors , 2019, J. Multivar. Anal..

[24]  P. Vieu,et al.  Nonparametric Functional Data Analysis: Theory and Practice (Springer Series in Statistics) , 2006 .

[25]  Tomasz Górecki,et al.  Selected statistical methods of data analysis for multivariate functional data , 2018 .

[26]  Han Lin Shang,et al.  High-dimensional functional time series forecasting: An application to age-specific mortality rates , 2018, J. Multivar. Anal..

[27]  Manuel Febrero-Bande,et al.  Goodness-of-fit tests for the functional linear model based on randomly projected empirical processes , 2017, The Annals of Statistics.

[28]  K. J. Utikal,et al.  Inference for Density Families Using Functional Principal Component Analysis , 2001 .

[29]  Henry W. Altland,et al.  Applied Functional Data Analysis , 2003, Technometrics.

[30]  Jane-Ling Wang,et al.  Review of Functional Data Analysis , 2015, 1507.05135.

[31]  Pedro Delicado,et al.  Functional k-sample problem when data are density functions , 2007, Comput. Stat..

[32]  Philippe Vieu,et al.  Methodological Richness of Functional Data Analysis , 2011 .

[33]  Philippe Vieu,et al.  On dimension reduction models for functional data , 2018 .

[34]  Heng Lian,et al.  Functional partial linear model , 2009, Journal of Nonparametric Statistics.

[35]  Hans-Georg Müller,et al.  Peter Hall, functional data analysis and random objects , 2016 .

[36]  Daniela Rodriguez,et al.  Partly linear models on Riemannian manifolds , 2010, 1003.1573.

[37]  Jane-Ling Wang,et al.  From sparse to dense functional data and beyond , 2016 .

[38]  Mustapha Rachdi,et al.  Data-driven kNN estimation in nonparametric functional data analysis , 2017, J. Multivar. Anal..

[39]  Fabian Scheipl,et al.  A general framework for functional regression modelling , 2017 .

[40]  Mariela Sued,et al.  The spatial sign covariance operator: Asymptotic results and applications , 2018, J. Multivar. Anal..

[41]  Julien Jacques,et al.  Functional data clustering: a survey , 2013, Advances in Data Analysis and Classification.

[42]  Wenceslao González-Manteiga,et al.  Statistics for Functional Data , 2007, Comput. Stat. Data Anal..

[43]  James O. Ramsay,et al.  Functional Data Analysis , 2005 .

[44]  S. Ejaz Ahmed,et al.  Big and complex data analysis: methodologies and applications , 2017 .

[45]  Jorge Mateu,et al.  Advances in spatial functional statistics , 2016, Stochastic Environmental Research and Risk Assessment.

[46]  José R. Berrendero,et al.  An RKHS model for variable selection in functional linear regression , 2019, J. Multivar. Anal..

[47]  James O. Ramsay,et al.  Spatial spline regression models , 2013 .

[48]  Alessia Pini,et al.  Multi-aspect local inference for functional data: Analysis of ultrasound tongue profiles , 2019, J. Multivar. Anal..

[49]  Sara van de Geer,et al.  Statistics for High-Dimensional Data: Methods, Theory and Applications , 2011 .

[50]  Pascal Sarda,et al.  Functional linear regression with points of impact , 2016, 1601.02798.

[51]  Wenceslao González-Manteiga,et al.  Functional Principal Component Regression and Functional Partial Least‐squares Regression: An Overview and a Comparative Study , 2017 .

[52]  Sylvie Viguier-Pla,et al.  Gap between orthogonal projectors - Application to stationary processes , 2016, J. Multivar. Anal..

[53]  Mayukh Dass,et al.  Introducing Functional Data Analysis to Managerial Science , 2012 .

[54]  Alejandro Cholaquidis,et al.  Multivariate and functional robust fusion methods for structured Big Data , 2019, J. Multivar. Anal..

[55]  Naâmane Laib,et al.  Nonparametric kernel regression estimation for functional stationary ergodic data: Asymptotic properties , 2010, J. Multivar. Anal..

[56]  Taras Bodnar,et al.  Exact and asymptotic tests on a factor model in low and large dimensions with applications , 2014, J. Multivar. Anal..

[57]  Alicia Nieto-Reyes,et al.  Statistical functional depth , 2017 .

[58]  Graciela Boente,et al.  Robust estimators in semi-functional partial linear regression models , 2017, J. Multivar. Anal..

[59]  Ingrid Van Keilegom,et al.  Two-sample tests in functional data analysis starting from discrete data , 2007 .

[60]  R. Serfling,et al.  General notions of statistical depth function , 2000 .

[61]  María Dolores Ruiz-Medina,et al.  Strongly consistent autoregressive predictors in abstract Banach spaces , 2018, J. Multivar. Anal..

[62]  Lajos Horváth,et al.  An introduction to functional data analysis and a principal component approach for testing the equality of mean curves , 2015, Revista Matemática Complutense.

[63]  Alessia Pini,et al.  The interval testing procedure: A general framework for inference in functional data analysis , 2016, Biometrics.

[64]  Philippe Vieu,et al.  Error variance estimation in semi-functional partially linear regression models , 2015 .

[65]  E. Masry.  Nonparametric regression estimation for dependent functional data: asymptotic normality , 2005 .

[66]  P. Vieu,et al.  Sparse nonparametric model for regression with functional covariate , 2016 .

[67]  Mohamed Chaouch.  Volatility estimation in a nonlinear heteroscedastic functional regression model with martingale difference errors , 2019, J. Multivar. Anal..

[68]  Laura M. Sangalli,et al.  The role of Statistics in the era of Big Data , 2018 .

[69]  Wolfgang Jank,et al.  Functional Data Analysis in Electronic Commerce Research , 2006, math/0609173.

[70]  Ricardo Fraiman,et al.  Feature selection for functional data , 2015, J. Multivar. Anal..

[71]  Philippe Vieu,et al.  kNN estimation in functional partial linear modeling , 2020 .

[72]  Philippe Vieu,et al.  Nonparametric modelling for functional data: selected survey and tracks for future , 2018, Statistics.

[73]  Sylvie Viguier-Pla,et al.  Commuter of operators in a Hilbert space , 2019, J. Multivar. Anal..

[74]  Badih Ghattas,et al.  Classifying densities using functional regression trees: Applications in oceanology , 2007, Comput. Stat. Data Anal..

[75]  Andr'e Mas,et al.  Linear Processes for Functional Data , 2009, Oxford Handbooks Online.

[76]  Enea G. Bongiorno,et al.  Describing the concentration of income populations by functional principal component analysis on Lorenz curves , 2019, J. Multivar. Anal..

[77]  Caroline F Finch,et al.  Applications of functional data analysis: A systematic review , 2013, BMC Medical Research Methodology.

[78]  J. Marron,et al.  Object Statistics on Curved Manifolds , 2017 .

[79]  Philippe Vieu,et al.  Partial linear modelling with multi-functional covariates , 2015, Comput. Stat..

[80]  Aldo Goia,et al.  An introduction to recent advances in high/infinite dimensional statistics , 2016, J. Multivar. Anal..

[81]  Enea G. Bongiorno,et al.  An introduction to the 4th edition of the International Workshop on Functional and Operatorial Statistics , 2017 .

[82]  Peter Filzmoser,et al.  Simplicial principal component analysis for density functions in Bayes spaces , 2016, Comput. Stat. Data Anal..

[83]  Jacopo Rossini,et al.  Quantifying prediction uncertainty for functional-and-scalar to functional autoregressive models under shape constraints , 2019, J. Multivar. Anal..

[84]  Mustapha Rachdi,et al.  Consistency of the regression estimator with functional data under long memory conditions , 2008 .

[85]  Alan J. Miller.  Subset Selection in Regression , 1992 .

[86]  Cedric Neumann,et al.  Review and application of functional data analysis to chemical data—The example of the comparison, classification, and database search of forensic ink chromatograms , 2015 .

[87]  Yufeng Liu,et al.  Comments on: Probability enhanced effective dimension reduction for classifying sparse functional data , 2016 .

[88]  D. Bosq.  Linear Processes in Function Spaces: Theory And Applications , 2000 .

[89]  T. Hsing,et al.  Theoretical foundations of functional data analysis, with an introduction to linear operators , 2015 .

[90]  Philippe Vieu,et al.  Variable selection in infinite-dimensional problems , 2014 .

[91]  Piotr Kokoszka,et al.  Dependent Functional Data , 2012 .

[92]  Lixing Zhu,et al.  Asymptotics, finite-sample comparisons and applications for two-sample tests with functional data , 2019, J. Multivar. Anal..

[93]  Piotr Kokoszka,et al.  Special issue on functional data analysis , 2017 .

[94]  Mariano J. Valderrama,et al.  An overview to modelling functional data , 2007, Comput. Stat..

[95]  Daniel Vogel,et al.  The spatial sign covariance matrix with unknown location , 2013, J. Multivar. Anal..

[96]  A. Cuevas.  A partial overview of the theory of statistics with functional data , 2014 .

[97]  Yuao Hu,et al.  Nonparametric Estimation of Variance Function for Functional Data Under Mixing Conditions , 2013 .

[98]  B. Sen,et al.  FRACTALS WITH POINT IMPACT IN FUNCTIONAL LINEAR REGRESSION. , 2010, Annals of statistics.

[99]  Philippe Vieu,et al.  Semi-functional partial linear regression , 2006 .

[100]  Alessia Pini,et al.  Interval-wise testing for functional data , 2017 .

[101]  Agustín Alvarez,et al.  Robust sieve estimators for functional canonical correlation analysis , 2019, J. Multivar. Anal..

[102]  Lajos Horváth,et al.  TESTING EQUALITY OF MEANS WHEN THE OBSERVATIONS ARE FROM FUNCTIONAL TIME SERIES , 2015 .

[103]  Jin-Ting Zhang,et al.  Analysis of Variance for Functional Data , 2013 .

[104]  Taras Bodnar,et al.  Spectral analysis of the Moore-Penrose inverse of a large dimensional sample covariance matrix , 2015, J. Multivar. Anal..

[105]  Piotr Kokoszka,et al.  Inference for Functional Data with Applications , 2012 .

[106]  Gery Geenens,et al.  Curse of dimensionality and related issues in nonparametric functional regression , 2011 .

[107]  P. Kokoszka,et al.  Introduction to Functional Data Analysis , 2017 .

[108]  Stanislav Nagy.  An overview of consistency results for depth functionals , 2017 .

[109]  T. Choi,et al.  Gaussian Process Regression Analysis for Functional Data , 2011 .

[110]  Nadia L. Kudraszow,et al.  Uniform consistency of kNN regressors for functional variables , 2013 .