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Statistical Inference, Econometric Analysis and Matrix Algebra

Statistical Inference, Econometric Analysis and Matrix AlgebraHans Joachim Werner and Ingram Olkin Part VII Special Topics Some Comments on Fisher’s αIndex of Diversity and on the

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Page 1: Statistical Inference, Econometric Analysis and Matrix AlgebraHans Joachim Werner and Ingram Olkin Part VII Special Topics Some Comments on Fisher’s αIndex of Diversity and on the

Statistical Inference, Econometric Analysisand Matrix Algebra

Page 2: Statistical Inference, Econometric Analysis and Matrix AlgebraHans Joachim Werner and Ingram Olkin Part VII Special Topics Some Comments on Fisher’s αIndex of Diversity and on the

Bernhard Schipp • Walter KrämerEditors

Statistical Inference,Econometric Analysisand Matrix Algebra

Festschrift in Honour of Götz Trenkler

ABC

Page 3: Statistical Inference, Econometric Analysis and Matrix AlgebraHans Joachim Werner and Ingram Olkin Part VII Special Topics Some Comments on Fisher’s αIndex of Diversity and on the

Editors

Prof. Dr. Bernhard SchippTU DresdenFakultät WirtschaftswissenschaftenProfessur für Quantitative Verfahren, insb.

ÖkonometrieMommsenstr. 1201062 [email protected]

Prof. Dr. Walter KrämerTU DortmundFakultät StatistikLehrstuhl für Wirtschafts-

und SozialstatistikVogelpothsweg 7844221 [email protected]

ISBN: 978-3-7908-2120-8 e-ISBN: 978-3-7908-2121-5

Library of Congress Control Number: 2008936140

c© 2009 Physica-Verlag Heidelberg

This work is subject to copyright. All rights are reserved, whether the whole or part of the material isconcerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting,reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publicationor parts thereof is permitted only under the provisions of the German Copyright Law of September 9,1965, in its current version, and permission for use must always be obtained from Springer. Violationsare liable to prosecution under the German Copyright Law.

The use of general descriptive names, registered names, trademarks, etc. in this publication does notimply, even in the absence of a specific statement, that such names are exempt from the relevant protectivelaws and regulations and therefore free for general use.

Cover design: WMXDesign GmbH, Heidelberg

Printed on acid-free paper

9 8 7 6 5 4 3 2 1

springer.com

Page 4: Statistical Inference, Econometric Analysis and Matrix AlgebraHans Joachim Werner and Ingram Olkin Part VII Special Topics Some Comments on Fisher’s αIndex of Diversity and on the

Prof. Dr. Götz Trenkler

Page 5: Statistical Inference, Econometric Analysis and Matrix AlgebraHans Joachim Werner and Ingram Olkin Part VII Special Topics Some Comments on Fisher’s αIndex of Diversity and on the

Preface

This Festschrift is dedicated to Götz Trenkler on the occasion of his 65th birthday.As can be seen from the long list of contributions, Götz has had and still has

an enormous range of interests, and colleagues to share these interests with. Heis a leading expert in linear models with a particular focus on matrix algebra inits relation to statistics. He has published in almost all major statistics and matrixtheory journals. His research activities also include other areas (like nonparametrics,statistics and sports, combination of forecasts and magic squares, just to mentiona few).

Götz Trenkler was born in Dresden in 1943. After his school years in East Ger-many and West-Berlin, he obtained a Diploma in Mathematics from Free Universityof Berlin (1970), where he also discovered his interest in Mathematical Statistics.In 1973, he completed his Ph.D. with a thesis titled: On a distance-generating func-tion of probability measures. He then moved on to the University of Hannover tobecome Lecturer and to write a habilitation-thesis (submitted 1979) on alternativesto the Ordinary Least Squares estimator in the Linear Regression Model, a topic thatwould become his predominant field of research in the years to come.

In 1983 Götz Trenkler was appointed Full Professor of Statistics and Economet-rics at the Department of Statistics at the University of Dortmund, where he contin-ues to teach and do research until today. He served as dean of the department from1987 to 1990 and declined an offer from Dresden University of Technology in 1993.He has been visiting Professor at the University of California at Berkeley, USA, andthe University of Tampere, Finland, and is a regular contributor to international con-ferences on matrix methods in statistics. Currently, he is the Coordinating Editor ofStatistical Papers, Associate Editor of several other international journals and re-cently the twice-in-a-row recipient of the best-teacher-award of the department.

Among Götz Trenkler’s extracurricular activities are tennis, chess and the com-pilation of a unique collection of Aphorisms in Statistics, samples of which can befound at the beginning of the chapters of this book. He certainly would do the sci-entific community a great service by having them published at some time.

The editors are grateful to all contributors, many of whom are not only scientificcolleagues but also his personal friends.

vii

Page 6: Statistical Inference, Econometric Analysis and Matrix AlgebraHans Joachim Werner and Ingram Olkin Part VII Special Topics Some Comments on Fisher’s αIndex of Diversity and on the

viii Preface

We express our appreciation for editorial and LATEX-assistance to Sabine Hege-wald, and in particular to Matthias Deutscher, who managed to edit successfullyalmost 30 manuscripts that were characterized by a great variety of individual pref-erences in style and layout, and to Alice Blanck and Werner A. Müller from SpringerPublishing for their support.

Dresden and Dortmund Bernhard SchippJuly 2008 Walter Krämer

Page 7: Statistical Inference, Econometric Analysis and Matrix AlgebraHans Joachim Werner and Ingram Olkin Part VII Special Topics Some Comments on Fisher’s αIndex of Diversity and on the

Contents

List of Contributors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii

Part I Nonparametric Inference

Adaptive Tests for the c-Sample Location Problem . . . . . . . . . . . . . . . . . . . . 3Herbert Büning

On Nonparametric Tests for Trend Detection in Seasonal Time Series . . . 19Oliver Morell and Roland Fried

Nonparametric Trend Tests for Right-Censored Survival Times . . . . . . . . . 41Sandra Leissen, Uwe Ligges, Markus Neuhäuser, and Ludwig A. Hothorn

Penalty Specialists Among Goalkeepers: A Nonparametric BayesianAnalysis of 44 Years of German Bundesliga . . . . . . . . . . . . . . . . . . . . . . . . . . 63Björn Bornkamp, Arno Fritsch, Oliver Kuss, and Katja Ickstadt

Permutation Tests for Validating Computer Experiments . . . . . . . . . . . . . . 77Thomas Mühlenstädt and Ursula Gather

Part II Parametric Inference

Exact and Generalized Confidence Intervals in the Common MeanProblem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85Joachim Hartung and Guido Knapp

Locally Optimal Tests of Independence for Archimedean CopulaFamilies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103Jörg Rahnenführer

ix

Page 8: Statistical Inference, Econometric Analysis and Matrix AlgebraHans Joachim Werner and Ingram Olkin Part VII Special Topics Some Comments on Fisher’s αIndex of Diversity and on the

x Contents

Part III Design of Experiments and Analysis of Variance

Optimal Designs for Treatment-Control Comparisons in MicroarrayExperiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115Joachim Kunert, R.J. Martin, and Sabine Rothe

Improving Henderson’s Method 3 Approach when Estimating VarianceComponents in a Two-way Mixed Linear Model . . . . . . . . . . . . . . . . . . . . . . 125Razaw al Sarraj and Dietrich von Rosen

Implications of Dimensionality on Measurement Reliability . . . . . . . . . . . . 143Kimmo Vehkalahti, Simo Puntanen, and Lauri Tarkkonen

Part IV Linear Models and Applied Econometrics

Robust Moment Based Estimation and Inference: The GeneralizedCressie–Read Estimator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163Ron C. Mittelhammer and George G. Judge

More on the F-test under Nonspherical Disturbances . . . . . . . . . . . . . . . . . 179Walter Krämer and Christoph Hanck

Optimal Estimation in a Linear Regression Model using IncompletePrior Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185Helge Toutenburg, Shalabh, and Christian Heumann

Minimum Description Length Model Selection in Gaussian Regressionunder Data Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201Erkki P. Liski and Antti Liski

Self-exciting Extreme Value Models for Stock Market Crashes . . . . . . . . . 209Rodrigo Herrera and Bernhard Schipp

Consumption and Income: A Spectral Analysis . . . . . . . . . . . . . . . . . . . . . . 233D.S.G. Pollock

Part V Stochastic Processes

Improved Estimation Strategy in Multi-Factor Vasicek Model . . . . . . . . . . 255S. Ejaz Ahmed, Sévérien Nkurunziza, and Shuangzhe Liu

Bounds on Expected Coupling Times in a Markov Chain . . . . . . . . . . . . . . 271Jeffrey J. Hunter

Multiple Self-decomposable Laws on Vector Spaces and on Groups:The Existence of Background Driving Processes . . . . . . . . . . . . . . . . . . . . . . 295Wilfried Hazod

Page 9: Statistical Inference, Econometric Analysis and Matrix AlgebraHans Joachim Werner and Ingram Olkin Part VII Special Topics Some Comments on Fisher’s αIndex of Diversity and on the

Contents xi

Part VI Matrix Algebra and Matrix Computations

Further Results on Samuelson’s Inequality . . . . . . . . . . . . . . . . . . . . . . . . . . 311Richard William Farebrother

Revisitation of Generalized and Hypergeneralized Projectors . . . . . . . . . . 317Oskar Maria Baksalary

On Singular Periodic Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325Jürgen Groß

Testing Numerical Methods Solving the Linear Least Squares Problem . . 333Claus Weihs

On the Computation of the Moore–Penrose Inverse of Matriceswith Symbolic Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 349Karsten Schmidt

On Permutations of Matrix Products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359Hans Joachim Werner and Ingram Olkin

Part VII Special Topics

Some Comments on Fisher’s ααα Index of Diversity and on the KazwiniCosmography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 369Oskar Maria Baksalary, Ka Lok Chu, Simo Puntanen, and George P. H.Styan

Ultimatum Games and Fuzzy Information . . . . . . . . . . . . . . . . . . . . . . . . . . 395Philip Sander and Peter Stahlecker

Are Bernstein’s Examples on Independent Events Paradoxical? . . . . . . . . 411Czesław Stepniak and Tomasz Owsiany

A Classroom Example to Demonstrate Statistical Concepts . . . . . . . . . . . . 415Dietrich Trenkler

Selected Publications of Götz Trenkler . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425

Page 10: Statistical Inference, Econometric Analysis and Matrix AlgebraHans Joachim Werner and Ingram Olkin Part VII Special Topics Some Comments on Fisher’s αIndex of Diversity and on the

List of Contributors

S. Ejaz Ahmed Department of Mathematics and Statistics, University of Windsor,401 Sunset Avenue, Windsor, ON, Canada N9B 3P4, [email protected]

Oskar Maria Baksalary Faculty of Physics, Adam Mickiewicz University, ul.Umultowska 85, 61-614 Poznan, Poland, [email protected]

Björn Bornkamp Fakultät Statistik, Technische Universität Dortmund, 44221Dortmund, Germany, [email protected]

Herbert Büning Freie Universität Berlin, 14195 Berlin, Germany,[email protected]

Ka Lok Chu Department of Mathematics, Dawson College, 3040 ouest, rueSherbrooke, Westmount, QC, Canada H3Z 1A4, [email protected]

Richard William Farebrother 11 Castle Road, Bayston Hill, Shrewsbury SY30NF, UK, [email protected]

Roland Fried Fakultät Statistik, Technische Universität Dortmund, 44221Dortmund, Germany, [email protected]

Arno Fritsch Fakultät Statistik, Technische Universität Dortmund, 44221Dortmund, Germany, [email protected]

Ursula Gather Fakultät Statistik, Technische Universität Dortmund, 44221Dortmund, Germany, [email protected]

Jürgen Groß Carl von Ossietzky Universität Oldenburg, Fakultät V, Institut fürMathematik, 26111 Oldenburg, Germany, [email protected]

Christoph Hanck Department Quantitative Economics, Universiteit Maastricht,6211 LM Maastricht, The Netherlands, [email protected]

Joachim Hartung Fakultät Statistik, Technische Universität Dortmund, 44221Dortmund, Germany, [email protected]

xiii

Page 11: Statistical Inference, Econometric Analysis and Matrix AlgebraHans Joachim Werner and Ingram Olkin Part VII Special Topics Some Comments on Fisher’s αIndex of Diversity and on the

xiv List of Contributors

Wilfried Hazod Fakultät für Mathematik, Technische Universität Dortmund, 44221Dortmund, Germany, [email protected]

Christian Heumann Institut für Statistik, Universität München, 80799 München,Germany, [email protected]

Rodrigo Herrera Fakultät Wirtschaftswissenschaften, Technische UniversitätDresden, 01062 Dresden, Germany, [email protected]

Ludwig A. Hothorn Institut für Biostatistik, Leibniz Universität Hannover, D-30419Hannover, Germany, [email protected]

Jeffrey J. Hunter Institute of Information & Mathematical Sciences, MasseyUniversity, Private Bag 102-904, North Shore Mail Centre, Auckland 0754, NewZealand, [email protected]

Katja Ickstadt Fakultät Statistik, Technische Universität Dortmund, 44221Dortmund, Germany, [email protected]

George G. Judge University of California-Berkeley, 207 Giannini Hall, Berkeley,CA 94720, [email protected]

Guido Knapp Fakultät Statistik, Technische Universität Dortmund, 44221Dortmund, Germany, [email protected]

Walter Krämer Fakultät Statistik, TU Dortmund, 44221 Dortmund, Germany,[email protected]

Joachim Kunert Fakultät Statistik, Technische Universität Dortmund, 44221Dortmund, Germany, [email protected]

Oliver Kuss Institut für Medizinische Epidemiologie, Biometrie und Informatik,Martin-Luther-Universität Halle-Wittenberg, 06097 Halle (Saale), Germany,[email protected]

Sandra Leissen Fakultät Statistik, Technische Universität Dortmund, 44221Dortmund, Germany, [email protected]

Uwe Ligges Fakultät Statistik, Technische Universität Dortmund, 44221 Dortmund,Germany, [email protected]

Antti Liski Tampere University of Technology, Tampere, Finland,[email protected]

Erkki P. Liski University of Tampere, Tampere, Finland, [email protected]

Shuangzhe Liu Faculty of Information Sciences and Engineering, University ofCanberra, Canberra ACT 2601, Australia, [email protected]

R.J. Martin Wirksworth, DE4 4EB, UK, [email protected]

Ron C. Mittelhammer School of Economic Sciences, Washington State University,101C Hulbert Hall, Pullman, WA 99164-6210, [email protected]

Page 12: Statistical Inference, Econometric Analysis and Matrix AlgebraHans Joachim Werner and Ingram Olkin Part VII Special Topics Some Comments on Fisher’s αIndex of Diversity and on the

List of Contributors xv

Oliver Morell Fakultät Statistik, Technische Universität Dortmund, 44221Dortmund, Germany, [email protected]

Thomas Mühlenstädt Fakultät Statistik, Technische Universität Dortmund, 44221Dortmund, Germany, [email protected]

Markus Neuhäuser Fachbereich Mathematik und Technik, RheinAhr-CampusRemagen, 53424 Remagen, Germany, [email protected]

Sévérien Nkurunziza Department of Mathematics and Statistics, University ofWindsor, 401 Sunset Avenue, Windsor, ON, Canada N9B 3P4,[email protected]

Ingram Olkin Department of Statistics, Sequoia Hall, 390 Serra Mall, StanfordUniversity, Stanford, CA 94305-4065, USA, [email protected]

Tomasz Owsiany Institute of Mathematics, University of Rzeszów, Al. Rejtana 16A, 35-959 Rzeszów, Poland, [email protected]

D.S.G. Pollock Department of Economic, University of Leicester, Leicester LE17RH, UK, [email protected]

Simo Puntanen Department of Mathematics and Statistics, University of Tampere,33014 Tampere, Finland, [email protected]

Jörg Rahnenführer Fakultät Statistik, Technische Universität Dortmund, 44221Dortmund, Germany, [email protected]

Sabine Rothe Fakultät Statistik, Technische Universität Dortmund, 44221Dortmund, Germany, [email protected]

Philip Sander Universität Hamburg, Institut für Statistik und Ökonometrie,Von-Melle-Park 5, 20146 Hamburg, Germany, [email protected]

Razaw al Sarraj Department of Energy and Technology, Box 7032, 750 07Uppsala, Sweden, [email protected]

Bernhard Schipp Fakultät Wirtschaftswissenschaften, Technische UniversitätDresden, 01062 Dresden, Germany, [email protected]

Karsten Schmidt Fakultät Wirtschaftswissenschaften, Fachhochschule Schmalka-lden, 98574 Schmalkalden, Germany, [email protected]

Shalabh Department of Mathematics & Statistics, Indian Institute of TechnologyKanpur, Kanpur 208016, India, [email protected], [email protected]

Peter Stahlecker Universität Hamburg, Institut für Statistik und Ökonometrie,Von-Melle-Park 5, 20146 Hamburg, Germany, [email protected]

Czesław Stepniak, Institute of Mathematics, University of Rzeszów, Al. Rejtana 16A, 35-959 Rzeszów, Poland, [email protected]

George P.H. Styan Department of Mathematics and Statistics, McGill University,1005-805 ouest, rue Sherbrooke, Montréal QC, Canada H3A 2K6,[email protected]

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xvi List of Contributors

Lauri Tarkkonen Department of Mathematics and Statistics, PO Box 54,University of Helsinki, 00014 Helsinki, Finland, [email protected]

Helge Toutenburg Institut für Statistik, Universität München, 80799 München,Germany, [email protected]

Dietrich Trenkler Fachbereich Wirtschaftswissenschaften, Universität Osnabrück,49069 Osnabrück, Germany, Dietrich.Trenkler@Uni-Osnabrück.de

Kimmo Vehkalahti Department of Mathematics and Statistics, PO Box 68,University of Helsinki, 00014 Helsinki, Finland, [email protected]

Dietrich von Rosen Department of Energy and Technology, Box 7032, 750 07Uppsala, Sweden, [email protected]

Claus Weihs Fakultät Statistik, Technische Universität Dortmund, 44221 Dortmund,Germany, [email protected]

Hans Joachim Werner Wirtschaftswissenschaftlicher Fachbereich, StatistischeAbteilung, Universität Bonn, 53113 Bonn, Germany, [email protected]