Modern Nonparametric, Robust and Multivariate Methods

Klaus Nordhausen • Sara Taskinen Editors

Modern Nonparametric, Robust and Multivariate Methods Festschrift in Honour of Hannu Oja

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Editors Klaus Nordhausen Department of Mathematics and Statistics University of Turku Turku, Finland School of Health Sciences University of Tampere Tampere, Finland

ISBN 978-3-319-22403-9 DOI 10.1007/978-3-319-22404-6

Sara Taskinen Department of Mathematics and Statistics University of JyvRaskylRa JyvRaskylRa, Finland

ISBN 978-3-319-22404-6 (eBook)

Library of Congress Control Number: 2015951385 Mathematics Subject Classification (2010): 62H10, 62H12, 62H15, 62H20, 62G10, 62G35, 92C55 Springer Cham Heidelberg New York Dordrecht London © Springer International Publishing Switzerland 2015 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper Springer International Publishing AG Switzerland is part of Springer Science+Business Media (www.springer.com)

Published with the kind permission of © Ritva Oja, 2011. All Rights Reserved.

Foreword

Hannu Oja has had an extensive and illustrious career. Many things are striking when you look back over the roughly 35 years of his scholarship. His work forms a unity and coherence, focusing on multivariate invariant and equivariant statistical methods. His work steadily evolved from his early results on defining an affine equivariant median, now referred to as the Oja median, in the early 1980s to an efficiently computable affine equivariant median using transform–retransform methods developed in the late 1990s. It has been my experience, and I am sure I speak for his many students and coauthors that he is the ideal collaborator. He always has insightful comments, is an excellent listener, and is generous to a fault. It has been a privilege and pleasure to work with him. Over a period of many years, I had the further pleasure of visiting Oulu, Tampere, and Jyväskylä to work on problems with Hannu as well as working with and knowing two of his finest students, Jyrki Möttönen and Esa Ollila, both of whom have gone on to impressive research careers. My interactions with Hannu began in the summer of 1989 when he visited Penn State for a week with Jukka Nyblom as they were on their way to an IMS meeting in Colorado. During that week, we combined some results of their work and some joint work of mine with Bruce Brown into a paper, On Certain Bivariate Tests and Medians, published in 1992 in the Journal of the American Statistical Association. Thus began a fruitful long-term relationship. In January 1991, Hannu brought his family to State College for 6 months and was a visiting professor in the statistics department at Penn State. It was not all work during that time. On spring break in March we all went on a driving trip, exploring the eastern part of the USA through Kentucky and then to Florida where in fine Finnish fashion the family could not wait to swim in the cold Atlantic Ocean. My overall goal here is to discuss the evolution of his research program for the development of multivariate methods beginning in the early 1980s with the publication of his 1983 paper, Descriptive Statistics for Multivariate Distributions, published in Statistics and Probability Letters and finish with some brief remarks on his current research interest in invariant coordinate selection (ICS) and independent component analysis (ICA). Along the way, I will mention a few of the initial papers vii

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that he published when moving into new research areas. Elsewhere in this volume there is a thorough analysis of his coauthors and a list of his publications. His vita will reveal an even wider scholarly effort, including consulting in biomedical research and signal processing. The 1983 descriptive statistics paper is based on the idea of defining a median by minimizing a sum of simplices determined by data points along with a parameter. In a series of papers, this basic idea was expanded to include affine invariant and equivariant sign and rank tests and estimates for various experimental designs. Computation, especially for high-dimensional data, remained problematic. This work is nicely summed up in his 1999 review paper, Affine Invariant Multivariate Sign and Rank Tests and Corresponding Estimates: A Review, published in the Scandinavian Journal of Statistics. A breakthrough occurred when he combined work on non-affine spatial methods developed in a 1995 paper with Jyrki Möttönen entitled Multivariate Spatial Sign and Rank Methods published in the Journal of Nonparametric Statistics with transform-retransform methods discussed in a 1998 paper written with Biman Chakraborty and Probal Chaudhuri entitled Operating Transformation-Retransformation on Spatial Median and Angle Test in Statistica Sinica. The result was a computationally efficient set of affine invariant and equivariant statistical methods. This work was further refined and elaborated in a 2004 paper with Ron Randles in Statistical Science entitled Multivariate Nonparametric Tests. These ideas are at the heart of his seminal 2010 monograph, Multivariate Nonparametric Methods with R. There is much of interest in this monograph. For example, there is an extensive discussion and development of scatter matrices, another of his research threads. Scatter matrices form the foundation of much of his current interests in ICA and ICS. An early work is his 2006 paper with Seija Sirkiä and Jan Eriksson entitled Scatter Matrices and Independent Component Analysis in the Austrian Journal of Statistics. In 2009, the paper Invariant Co-ordinate Selection published in the Journal of the Royal Statistical Society, Series B and written with David Tyler, Frank Critchley, and Lutz Dümbgen greatly expanded the framework for this area and brought it to the attention of many more researchers in statistics. Currently, he has ongoing research projects involving the extension and application of ICA to time series and functional data. From 2008 to 2012, he was an Academy Professor in Finland, a richly deserved honor. If you consider the number of coauthors and their various countries and affiliations, you would conclude that Hannu is a major ambassador for Finland. State College, PA, USA May 2015

Tom Hettmansperger

Preface

This Festschrift contains a collection of articles dedicated to Hannu Oja, Professor of Statistics at the University of Turku, on the occasion of his 65th birthday. Hannu can be regarded as one of the most influential statisticians in Finland. His research career has been exceptional. Hannu has served as Professor in the Universities of Jyväskylä, Tampere and Turku, and as Visiting Professor at the Pennsylvania State University, University of Bern and Moscow State University. He has held several appointments granted by the Academy of Finland including the highly respected Academy Professorship in 2008–2012. Besides being an excellent researcher, Hannu is also an enjoyable teacher. He is a desired speaker at international statistics conferences and a wanted guest lecturer. Hannu takes supervision very seriously, providing excellent guidance and mentoring in all aspects required. Up to date, he has supervised eleven PhD theses—and is still supervising many new promising talents. Interestingly, almost all of Hannu’s PhD students have preferred an academic career over a non-academic one. This must have something to do with Hannu’s exemplary career and endless positive attitude towards statistics research. This book consists of 27 contributions written by Hannu’s former students, coauthors, colleagues and friends. The book is divided into four parts. Part I starts with some remarks about Hannu’s early career, given by his PhD thesis supervisor Professor (emeritus) Elja Arjas, followed by a light introduction to Hannu’s publications and coauthors. The remaining three parts of the book cover a wide variety of topics related to Hannu’s research interests. In Part II, some recent results in the areas of univariate nonparametric and robust methods are presented. Part III consists of papers concerning modern nonparametric and robust methods in the context of multivariate and functional data. Finally, Part IV is related to Hannu’s current research interest on Invariant Coordinate Selection. Also, two contributions on robust methods in signal processing applications are given. We wish to thank all the authors for their interesting contributions and smooth cooperation during the past 1.5 years. The feedback from the authors has been very positive and we have been pleased to see how every one we asked has been willing to show their gratitude to Hannu via this Festschrift. Our special thanks ix

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go furthermore to those who acted as referees for the contributions. The schedule was occasionally very tight, so without their output, we would not have managed to finish this Festschrift in time. In this context, we would also like to thank Veronika Rosteck from Springer who encouraged us throughout this project and provided help and assistance whenever needed. Our biggest thanks naturally belong to Hannu who taught us this profession and is still encouraging us on our scientific journey. We hope that his enthusiasm for statistics will continue for a long time and that he will remain an active member of our community. Tampere, Finland Jyväskylä, Finland June 2015

Klaus Nordhausen Sara Taskinen

Acknowledgements

Contributions 2 to 27 of this festschrift are peer-reviewed. We would like to thank all of the following referees for their excellent work: Arslan, Olcay Christmann, Andreas Datta, Somnath Frahm, Gabriel Hallin, Marc Hössjer, Ola Ilmonen, Pauliina Kassam, Saleem Larocque, Denis Möttönen, Jyrki Ollila, Esa Rousseeuw, Peter Satten, Glen Tyler, David Van Bever, Germain Villa-Vialaneix, Nathalie Zamar, Ruben

Bing, Li Critchley, Frank Filzmoser, Peter Fried, Roland Hettmansperger, Tom Hubert, Mia Jureˇcková, Jana Kent, John Ley, Christophe Nevalainen, Jaakko Paindaveine, Davy Ruiz-Gazen, Anne Serfling, Robert Valkonen, Tuomo Verdebout, Thomas Vogel, Daniel Zuo, Yijun

Chakraborty, Anirvan Croux, Christophe Fischer, Daniel Ghosh, Anil Hörmann, Siegfried Hunter, David Karvanen, Juha Konietschke, Frank Miettinen, Jari Nyblom, Jukka Pawlowsky-Glahn, Vera Sabolova, Radka Tarr, Garth Van Aelst, Stefan Wied, Dominik Yohai, Victor

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Contents

Part I 1

2

When We Were Very Young: Some Recollections from Hannu Oja’s First Years of Academic Life . . . .. . . . . . . . . . . . . . . . . . . . Elja Arjas Publication and Coauthorship Networks of Hannu Oja . . . . . . . . . . . . . . . Daniel Fischer, Klaus Nordhausen, and Sara Taskinen

Part II 3

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Remarks About Hannu Oja’s Career and Publications 3 7

Univariate Nonparametric and Robust Methods

Approximate U-Statistics for State Waiting Times Under Right Censoring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . Somnath Datta, Douglas J. Lorenz, and Susmita Datta

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Nonparametric Location Estimators in the Randomized Complete Block Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . Stefanie Hayoz and Jürg Hüsler

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5

Permutation Tests in Linear Regression . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . Jukka Nyblom

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Highly Robust and Highly Finite Sample Efficient Estimators for the Linear Model. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . Ezequiel Smucler and Víctor J. Yohai

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Optimal Rank Tests for Symmetry Against Edgeworth-Type Alternatives . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 109 Delphine Cassart, Marc Hallin, and Davy Paindaveine

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Generalized MM-Tests for Symmetry .. . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 133 Jue Wang and David E. Tyler

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Part III 9

Nonparametric and Robust Methods for Multivariate and Functional Data

M-Estimators of the Correlation Coefficient for Bivariate Independent Component Distributions . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 151 Georgy Shevlyakov and Pavel Smirnov

10 Robust Coordinates for Compositional Data Using Weighted Balances.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 167 Peter Filzmoser and Karel Hron 11 Computation of the Oja Median by Bounded Search . . . . . . . . . . . . . . . . . . 185 Karl Mosler and Oleksii Pokotylo 12 Algorithms for the Spatial Median . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 205 John T. Kent, Fikret Er, and Patrick D.L. Constable 13 L1 -Regression for Multivariate Clustered Data . . . .. . . . . . . . . . . . . . . . . . . . 225 Jaakko Nevalainen and Denis Larocque 14 Robust Variable Selection and Coefficient Estimation in Multivariate Multiple Regression Using LAD-Lasso . . . . . . . . . . . . . . . . 235 Jyrki Möttönen and Mikko J. Sillanpää 15 On Some Nonparametric Classifiers Based on Distribution Functions of Multivariate Ranks . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 249 Olusola Samuel Makinde and Biman Chakraborty 16 Robust Change Detection in the Dependence Structure of Multivariate Time Series. . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 265 Daniel Vogel and Roland Fried 17 Tyler’s M-Estimator in High-Dimensional Financial-Data Analysis .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 289 Gabriel Frahm and Uwe Jaekel 18 Affine Equivariant Rank-Weighted L-Estimation of Multivariate Location .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 307 Pranab Kumar Sen, Jana Jureˇcková, and Jan Picek 19 Robust High-Dimensional Precision Matrix Estimation . . . . . . . . . . . . . . 325 Viktoria Öllerer and Christophe Croux 20 Paired Sample Tests in Infinite Dimensional Spaces . . . . . . . . . . . . . . . . . . . . 351 Anirvan Chakraborty and Probal Chaudhuri 21 Semiparametric Analysis in Conditionally Independent Multivariate Mixture Models . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 371 Tracey W. Hammel, Thomas P. Hettmansperger, Denis H.Y. Leung, and Jing Qin

Contents

Part IV

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Invariant Coordinate Selection and Related Methods

22 A B-Robust Non-Iterative Scatter Matrix Estimator: Asymptotics and Application to Cluster Detection Using Invariant Coordinate Selection . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 395 Mohamed Fekri and Anne Ruiz-Gazen 23 On ANOVA-Like Matrix Decompositions . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 425 Giuseppe Bove, Frank Critchley, Radka Sabolova, and Germain Van Bever 24 On Invariant Within Equivalence Coordinate System (IWECS) Transformations . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 441 Robert Serfling 25 Alternative Diagonality Criteria for SOBI. . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 455 Jari Miettinen 26 Robust Simultaneous Sparse Approximation . . . . . . .. . . . . . . . . . . . . . . . . . . . 471 Esa Ollila 27 Nonparametric Detection of Complex-Valued Cyclostationary Signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 491 Visa Koivunen and Jarmo Lundén

Contributors

Elja Arjas Department of Mathematics and Statistics, University of Helsinki, Helsinki, Finland Giuseppe Bove Dipartimento di Scienze della Formazione, Università degli Studi Roma Tre, Roma, Italy Delphine Cassart ECARES, Université Libre de Bruxelles, Bruxelles, Belgium Anirvan Chakraborty Theoretical Statistics and Mathematics Unit, Indian Statistical Institute, Kolkata, India Biman Chakraborty School of Mathematics, University of Birmingham, Birmingham, UK Probal Chaudhuri Theoretical Statistics and Mathematics Unit, Indian Statistical Institute, Kolkata, India Patrick D.L. Constable Stony Lodge, Holwell, Sherborne, Dorset, UK Frank Critchley Department of Mathematics and Statistics, The Open University, Buckinghamshire, UK Christophe Croux Faculty of Economics and Business, KU Leuven, Leuven, Belgium Somnath Datta Department of Biostatistics, University of Florida, Gainesville, FL, USA Susmita Datta Department of Biostatistics, University of Florida, Gainesville, FL, USA Fikret Er Open Education Faculty, Yunusemre Campus, Anadolu University, Eskisehir, Turkey Mohamed Fekri Département de Mathématiques, Informatique et Réseaux, Institut National des Postes et Télécommunications, Rabat, Maroc

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Peter Filzmoser Institute of Statistics and Mathematical Methods in Economics, Vienna University of Technology, Vienna, Austria Daniel Fischer Natural Resources Institute Finland (Luke), Green Technology, Jokioinen, Finland School of Health Sciences, University of Tampere, Tampere, Finland Gabriel Frahm Department of Mathematics/Statistics, Helmut Schmidt University/University of the Federal Armed Forces Germany, Hamburg, Germany Roland Fried Fakultät Statistik, Technische Universität Dortmund, Dortmund, Germany Marc Hallin ECARES, Université Libre de Bruxelles, Bruxelles, Belgium ORFE, Princeton University, Princeton, NJ, USA Tracey W. Hammel Department of Statistics, Penn State University, University Park, PA, USA Stefanie Hayoz Institute of Mathematical Statistics and Actuarial Science, University of Bern, Bern, Switzerland Now at Statistics Unit, Swiss Group for Clinical Cancer Research (SAKK), Bern, Switzerland Thomas P. Hettmansperger Department of Statistics, Penn State University, University Park, PA, USA Karel Hron Department of Mathematical Analysis and Applications of Mathematics, Palacký University, Olomouc, Czech Republic Jürg Hüsler Institute of Mathematical Statistics and Actuarial Science, University of Bern, Bern, Switzerland Uwe Jaekel Department of Mathematics and Technology, University of Applied Sciences Koblenz, Remagen, Germany Jana Jureˇcková Faculty of Mathematics and Physics, Department of Probability and Statistics, Charles University, Prague 8, Czech Republic John T. Kent Department of Statistics, University of Leeds, Leeds, UK Visa Koivunen Department of Signal Processing and Acoustics, Aalto University, Aalto, Finland Denis Larocque Department of Decision Sciences, HEC Montréal, Montréal, QC, Canada Denis H.Y. Leung School of Economics, Singapore Management University, Singapore, Singapore

Contributors

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Douglas J. Lorenz Department of Bioinformatics and Biostatistics, University of Louisville, Louisville, KY, USA Jarmo Lundén Department of Signal Processing and Acoustics, Aalto University, Aalto, Finland Olusola Samuel Makinde School of Mathematics, University of Birmingham, Birmingham, UK Jari Miettinen Department of Mathematics and Statistics, University of Jyväskylä, Jyväskylä, Finland Karl Mosler Institute of Econometrics and Statistics, University of Cologne, Köln, Germany Jyrki Möttönen Department of Social Research, University of Helsinki, Helsinki, Finland Jaakko Nevalainen School of Health Sciences, University of Tampere, Tampere, Finland Klaus Nordhausen Department of Mathematics and Statistics, University of Turku, Turku, Finland School of Health Sciences, University of Tampere, Tampere, Finland Jukka Nyblom Department of Mathematics and Statistics, University of Jyväskylä, Jyväskylä, Finland Viktoria Öllerer Faculty of Economics and Business, KU Leuven, Leuven, Belgium Esa Ollila Department of Signal Processing and Acoustics, Aalto University, Espoo, Finland Davy Paindaveine ECARES and Department of Mathematics, Université Libre de Bruxelles, Bruxelles, Belgium Jan Picek Department of Applied Mathematics, Technical University of Liberec, Liberec, Czech Republic Oleksii Pokotylo Cologne Graduate School, University of Cologne, Köln, Germany Jing Qin Biostatistics Research Branch, National Institute of Allergy and Infectious Diseases, Bethesda, MA, USA Anne Ruiz-Gazen Toulouse School of Economics, Université Toulouse 1 Capitole, Toulouse, France Radka Sabolova Department of Mathematics and Statistics, The Open University, Buckinghamshire, UK

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Contributors

Pranab Kumar Sen Departments of Statistics and Biostatistics, University of North Carolina at Chapel Hill, Chapel Hill, NC, USA Robert Serfling Department of Mathematical Sciences, University of Texas at Dallas, Richardson, TX, USA Georgy Shevlyakov Institute of Applied Mathematics and Mechanics, Peter the Great St. Petersburg Polytechnic University, St. Petersburg, Russia Mikko J. Sillanpää Department of Mathematical Sciences and Biocenter Oulu, University of Oulu, Oulu, Finland Pavel Smirnov Institute of Applied Mathematics and Mechanics, Peter the Great St. Petersburg Polytechnic University, St. Petersburg, Russia Ezequiel Smucler Instituto de Cálculo, Universidad de Buenos Aires, Buenos Aires, Argentina Sara Taskinen Department of Mathematics and Statistics, University of Jyväskylä, Jyväskylä, Finland David E. Tyler Department of Statistics and Biostatistics, Rutgers – The State University of New Jersey, New Brunswick, NJ, USA Germain Van Bever Department of Mathematics and Statistics, The Open University, Buckinghamshire, UK Daniel Vogel Institute for Complex Systems and Mathematical Biology, University of Aberdeen, Aberdeen, UK Jue Wang Department of Statistics and Biostatistics, Rutgers – The State University of New Jersey, New Brunswick, NJ, USA Víctor J. Yohai Departamento de Matemáticas and Instituto de Cálculo, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires, Argentina