Advances in Multivariate Statistical Methods Statistical Science and Interdisciplinary Research Series Editor: Sankar K. Pal (Indian Statistical Institute) Description: In conjunction with the Platinum Jubilee celebrations of the Indian Statistical Institute, a series of books will be produced to cover various topics, such as Statistics and Mathematics, Computer Science, Machine Intelligence, Econometrics, other Physical Sciences, and Social and Natural Sciences. This series of edited volumes in the mentioned disciplines culminate mostly out of significant events — conferences, workshops and lectures — held at the ten branches and centers of ISI to commemorate the long history of the institute. Vol. 1 Mathematical Programming and Game Theory for Decision Making edited by S. K. Neogy, R. B. Bapat, A. K. Das & T. Parthasarathy (Indian Statistical Institute, India) Vol. 2 Advances in Intelligent Information Processing: Tools and Applications edited by B. Chandra & C. A. Murthy (Indian Statistical Institute, India) Vol. 3 Algorithms, Architectures and Information Systems Security edited by Bhargab B. Bhattacharya, Susmita Sur-Kolay, Subhas C. Nandy & Aditya Bagchi (Indian Statistical Institute, India) Vol. 4 Advances in Multivariate Statistical Methods edited by A. SenGupta (Indian Statistical Institute, India) Vol. 5 New and Enduring Themes in Development Economics edited by B. Dutta, T. Ray & E. Somanathan (Indian Statistical Institute, India) Vol. 6 Modeling, Computation and Optimization edited by S. K. Neogy, A. K. Das and R. B. Bapat (Indian Statistical Institute, India) RokTing - Advs in Multivariat Statistical.pmd 2 9/15/2009, 11:33 AM Platinum Jubilee Series Statistical Science and Interdisciplinary Research - Vol. 4 Advances in Multivariate Statistical Methods Editor Ashis SenGupta Indian Statistical Institute, India Series Editor: Sankar K. Pal World Scientific NEW JERSEY • LONDON • SINGAPORE • BEIJING • SHANGHAI • HONG KONG • TAIPEI • CHENNAI Published by World Scientific Publishing Co. Pte. Ltd. 5 Toh Tuck Link, Singapore 596224 USA office: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601 UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. Statistical Science and Interdisciplinary Research — Vol. 4 ADVANCES IN MULTIVARIATE STATISTICAL METHODS Copyright © 2009 by World Scientific Publishing Co. Pte. Ltd. All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher. For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher. ISBN-13 978-981-283-823-0 ISBN-10 981-283-823-6 Printed in Singapore. RokTing - Advs in Multivariat Statistical.pmd 1 9/15/2009, 11:33 AM September15,2009 11:46 WorldScientificReviewVolume-9inx6in AdvancesMultivariate Foreword TheIndianStatisticalInstitute(ISI)wasestablishedon17thDecember,1931by agreatvisionaryProf. PrasantaChandraMahalanobistopromoteresearchinthe theoryandapplicationsofstatisticsasanewscientificdisciplineinIndia.In1959, PanditJawaharlalNehru,thethenPrimeMinisterofIndiaintroducedtheISIAct in the parliament and designated it as an Institution of National Importance be- causeofitsremarkableachievementsinstatisticalworkaswellasitscontribution toeconomicplanning. Today,theIndianStatisticalInstituteoccupiesaprestigiouspositionintheaca- demicfirmament. Ithasbeenahavenforbrightandtalentedacademicsworking inanumberofdisciplines. ItsresearchfacultyhasdoneIndiaproudinthearenas of Statistics, Mathematics, Economics, Computer Science, among others. Over seventyfiveyears,ithasgrownintoamassivebanyantree,liketheinstituteem- blem.TheInstitutenowservesthenationasaunifiedandmonolithicorganization from different places, namely Kolkata, the Head Quarter, Delhi and Bangalore, two centers, a network of six SQC-OR Units located at Mumbai, Pune, Baroda, Hyderabad,ChennaiandCoimbatore,andabranch(fieldstation)atGiridih. The platinum jubilee celebrations of ISI have been launched by Honorable PrimeMinisterProf. ManmohanSinghonDecember24,2006,andtheGovern- mentofIndiahasdeclared29thJuneasthe“StatisticsDay”tocommemoratethe birthdayofProf. Mahalanobisnationally. Prof. Mahalanobiswasagreatbelieverininterdisciplinaryresearch,because hethoughtthatthiswillpromotethedevelopmentofnotonlyStatistics,butalso theothernaturalandsocialsciences.Topromoteinterdisciplinaryresearch,major strides were made in the areas of computer science, statistical quality control, economics,biologicalandsocialsciences,physicalandearthsciences. TheInstitute’smottoof“unityindiversity”hasbeentheguidingprincipleof all its activities since its inception. It highlights the unifying role of statistics in relationtovariousscientificactivities. In tune with this hallowed tradition, a comprehensive academic programme, involvingNobelLaureates,FellowsoftheRoyalSociety,AbelPrizewinnerand v September15,2009 11:46 WorldScientificReviewVolume-9inx6in AdvancesMultivariate vi Foreword other dignitaries, has been implemented throughout the Platinum Jubilee year, highlightingtheemergingareasofongoingfrontlineresearchinitsvariousscien- tificdivisions, centers,andoutlyingunits. Itincludesinternationalandnational- levelseminars,symposia,conferencesandworkshops,aswellasseriesofspecial lectures. As an outcome of these events, the Institute is bringing out a series of comprehensivevolumesindifferentsubjectsunderthetitleStatisticalScienceand InterdisciplinaryResearch,publishedbyWorldScientific,Singapore. The present volume titled “Advances in Multivariate Statistical Methods” is the fourth one in the series, and is also a special tribute to mark the birth cente- nary of Prof. S.N. Roy, who has greatly contributed to the aforesaid theme area ofthebookandenrichedthetrainingprogramsofISIasamemberoftheresearch teamofProf. Mahalanobis. Thevolumeconsistsoftwentysevenchapters,writ- tenbyeminentscientistsandexperiencedresearchersfromdifferentpartsofthe world. The chapters deal with both theory and applications covering the topics likelargedimensionaldataanalysis,directionaldataanalysis,clustering,estima- tion,distributiontheory,Bayesianinference,reliabilityanalysis,samplesurveys, and bioinformatics. Excellent reviews mentioning the challenging problems in somethrustarease.g.,largedimension-smallsamplesizewhichhastremendous applicationsindataminingandbioinformatics, arealsoaddressed. Ibelievethe state-of-theartstudiespresentedinthisbookwillbeveryusefultoreaders. Thankstothecontributorsfortheirexcellentresearchcontributions,andtothe volumeeditorProf. AshisSenGuptaandtheinvitededitorProf. BarryArnoldfor theirsincereeffortinbringingoutthevolumenicelyintime. Initialdesignofthe coverbyMr. IndranilDuttaisacknowledged. SincereeffortsbyProf. DilipSaha andDr.BarunMukhopadhyayforeditorialassistanceareappreciated.Thanksare alsoduetoWorldScientificfortheirinitiativeinpublishingtheseriesandbeinga partofthePlatinumJubileeendeavoroftheInstitute. April2008 SankarK.Pal Kolkata SeriesEditorand Director,ISI September15,2009 11:46 WorldScientificReviewVolume-9inx6in AdvancesMultivariate Preface Theyear2006markedthePlatinumJubileeofIndianStatisticalInstitute(ISI).ISI hasplayedaseminalroleinpromotingstatisticsingeneralworldwide. Aleading andsignificantcontributionofISIhasbeenintheareaofMultivariateStatistical MethodsaspresentedbyProf. P.C.Mahalanobisandhisteamofresearchersfrom theverygenesisofISI.Ofthem,Prof. SamarendraNathRoyproducedrealgems, throughhisresearchondifficultandinterestingproblems,suchasp-statisticsand joint distribution of roots of certain Wishart matrices, Union-intersection testing principle, Growth curve analysis, Categorical data analysis. The year 2006 also markedthebirthcentenaryofProfessorS.N.Roy. Itwasthusfeltthatacelebra- tionofthesetwosimultaneouseventsbemadeintheformofaWorkshopanda Conference on Multivariate Statistical Methods, focusing on its recently emerg- ingareasoftheoryandapplications. TheInternationalConferencewashelddur- ing December 28-29, 2006, at Kolkata. The conference was organized jointly by Profs. Barry C. Arnold, University of California, Riverside, USA, and Ashis SenGupta, IndianStatisticalInstitute, Kolkata, India, andwasattendedbyabout 150researchers. Thetopics,intunewiththethemeoftheconference,covereda widespectrum-asnapshotincludesDistributionTheory,StochasticEigenAnal- ysis, Multiple Testing Procedures, Longitudinal Data Analysis, Large p - Small n,RobustInference,DirectionalDataAnalysis,BayesianInference,Bioinformat- ics,CategoricalDataandClinicalTrials,RankingandSelection,Spatio-Temporal DataAnalysis,Econometrics,StatisticalProcessControl. Thisvolumeisnumber4intheseriesformedfromtheeventscelebratingthe PlatinumJubileeofISIwhichisbeingpublishedbyWorldScientific.Itpresentsa collectionof27invitedpapersbyinternationalluminariesinthesaidspirit,which emanatedfromtheConference,andwerepeer-reviewedandedited. Thechapters reflect advances in both theory and applications of multivariate statistical meth- ods. Thefirstfivechaptersdealwiththeanalysisoflargedimensionaldata. The firstchapterappealstotheUnion-IntersectionprincipledevelopedbyProf. S.N. Roy, and is thus a fitting tribute to him also. The challenging area of Large p - Small n, which is currently receiving great attention, is dealt with in Chapters 1 vii September15,2009 11:46 WorldScientificReviewVolume-9inx6in AdvancesMultivariate viii Preface and2. ThesearefollowedbythechapteronClusteringmethodsandtwochapters on Bioinformatics. Chapters 6 and 7 deal with models and inference for Direc- tional Data. Chapter 8 presents some elegant results on Characterization using regression. Chapters 9-11, present reviews and recent results related to multi- variateDistributionTheory. Chapters12-14,considerEstimation,whileChapters 15-17dealwithTestingofHypothesesproblems,illustratedbyvariousexamples fromappliedsciences.BayesianMethodsarehavingagreatimpactonanalysisof multivariatedataandthisfactisenhancedthroughChapters18-21,whichreflect onboththeoryandapplications.Thelastfivechaptersdealmainlywithmultivari- ate statistical methods in several real-life applications. Chapters 22-24 consider theareaofReliabilityAnalysis,Chapters25and26dealwithapplicationsofmul- tivariate techniques for analysis of some special types of time series data which areofrecentlyemergingnatureandinterest. Finally,Chapter27enhancesmulti- variatemethodsinSampleSurveys. WearethankfultoIndianStatisticalInstituteforpartialfinancialsupportand also to Institute of Mathematical Statistics, USA, for co-sponsoring it. We ac- knowledgewiththanksthesupportreceivedfromCalcuttaMathematicalSociety, ForumforInterdisciplinaryMathematics, IndianBayesianSociety, IndianAsso- ciationofProductivity,QualityandReliability,andInternationalIndianStatistical Association. Itisapleasuretothank,Prof. SankarK.Pal,DirectorofISI,forhis supportandencouragements.WealsothanktheMembersoftheInternationalAd- visoryCommittee,ProfessorsJ.K.Ghosh,K.V.Mardia,S.P.Mukherjee,P.K.Sen and K. Shimizu, for their advice with the editorial work of this volume. We are indeed grateful to the referees for their cooperation and scholarly reports on the paperstheyhavereviewed.Thelistofsuchrefereesincludes:ProfessorsArunAd- hikary, Sourabh Bhattacharya*, Subir Bhandari*, Arijit Chakraborty, Asis Chat- topadhyay,AjitChaturvedi,SamarjitDas,B.K.Kale,ShogoKato,ArnabLaha*, H.K. Tony Ng, Chandranath Pal, Arthur Pewsey*, R.N. Rattihalli*, T. Samanta, P.G. Sankaran, M.S. Sreehari and T.S. Vasulu (*indicates Referee for multiple papers). We also thank Mr. Prabhat Roy and Mr. Indranil Dutta for their help withtheprocessingofthisvolume. Lastbutnottheleast,weareindeedthankful toallauthorsforcomtributingscholarlypaperswhichhavegreatlyenrichedthis volume. September15,2009 11:46 WorldScientificReviewVolume-9inx6in AdvancesMultivariate Preface ix Wepresentthisvolume,intheseriescelebratingthePlatinumJubileeofISI, asaspecialtributetomarkthebirthcentenaryofProf. S.N.Roy,whohasgreatly enriched the research and teaching programs of ISI. It is hoped that this volume willserveasausefulandtimelyresourcemonographtotheresearchersandprac- titionersforadvancesintheareaofMultivariateStatisticalMethods. BarryC.Arnold AshisSenGupta InvitedEditor Editor DistinguishedProfessor ProfessorandHead DepartmentofStatistics AppliedStatisticsUnit UniversityofCalifornia IndianStatisticalInstitute Riverside,USA Kolkata,India April2008 April2008 Riverside Kolkata