Table Of ContentAdvances 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
