AMatrixHandbookforStatisticians

Acomprehensive,must-havehandbookofmatrixmethodswithauniqueemphasisonstatisticalapplicationsThistimelybook,AMatrixHandbookforStatisticians,providesacomprehensive,encyclopedictreatmentofmatricesastheyrelatetobothstatisticalconceptsandmethodologies.Writtenbyanexperiencedauthorityonmatricesandstatisticaltheory,thishandbookisorganizedbytopicratherthanmathematicaldevelopmentsandincludesnumerousreferencestoboththetheorybehindthemethodsandtheapplicationsofthemethods.Auniformapproachisappliedtoeachchapter,whichcontainsfourparts:adefinitionfollowedbyalistofresults;ashortlistofreferencestorelatedtopicsinthebook;oneormorereferencestoproofs;andreferencestoapplications.Theuseofextensivecross-referencingtotopicswithinthebookandexternalreferencingtoproofsallowsfordefinitionstobelocatedeasilyaswellasinterrelationshipsamongsubjectareastoberecognized.AMatrixHandbookforStatisticiansaddressestheneedformatrixtheorytopicstobepresentedtogetherinonebookandfeaturesacollectionoftopicsnotfoundelsewhereunderonecover.Thesetopicsinclude:ComplexmatricesAwiderangeofspecialmatricesandtheirpropertiesSpecialproductsandoperators,suchastheKroneckerproductPartitionedandpatternedmatricesMatrixanalysisandapproximationMatrixoptimizationMajorizationRandomvectorsandmatricesInequalities,suchasprobabilisticinequalitiesAdditionaltopics,suchasrank,eigenvalues,determinants,norms,generalizedinverses,linearandquadraticequations,differentiation,andJacobians,arealsoincluded.Thebookassumesafundamentalknowledgeofvectorsandmatrices,maintainsareasonablelevelofabstractionwhenappropriate,andprovidesacomprehensivecompendiumoflinearalgebraresultswithuseorpotentialuseinstatistics.AMatrixHandbookforStatisticiansisanessential,one-of-a-kindbookforgraduate-levelcoursesinadvancedstatisticalstudiesincludinglinearandnonlinearmodels,multivariateanalysis,andstatisticalcomputing.Italsoservesasanexcellentself-studyguideforstatisticalresearchers.