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1、BiometrikaTrustPartialLikelihoodAuthor(s):D.R.CoxReviewedwork(s):Source:Biometrika,Vol.62,No.2(Aug.,1975),pp.269-276Publishedby:BiometrikaTrustStableURL:http://www.jstor.org/stable/2335362.Accessed:20/12/201107:33YouruseoftheJSTORarchiveindicatesyouracceptanceoftheTerms&ConditionsofUse,avail
2、ableat.http://www.jstor.org/page/info/about/policies/terms.jspJSTORisanot-for-profitservicethathelpsscholars,researchers,andstudentsdiscover,use,andbuilduponawiderangeofcontentinatrusteddigitalarchive.Weuseinformationtechnologyandtoolstoincreaseproductivityandfacilitatenewformsofscholarship.
3、FormoreinformationaboutJSTOR,pleasecontactsupport@jstor.org.BiometrikaTrustiscollaboratingwithJSTORtodigitize,preserveandextendaccesstoBiometrika.http://www.jstor.orgBiometrika(1975),62,2,p.269269PrintedinGreatBritainPartiallikelihoodBYD.R.COXDepartmentofMathematics,ImperialCollege,LondonSUM
4、MARYAdefinitionisgivenofpartiallikelihoodgeneralizingtheideasofconditionalandmarginallikelihood.Applicationsincludelifetablesandinferenceinstochasticprocesses.Itisshownthattheusuallarge-samplepropertiesofmaximumlikelihoodestimatesandtestsapplywhenpartiallikelihoodisused.Somekeywords:Asymptot
5、ictheory;Censoring;Conditionallikelihood;Lifetable;Marginallikelihood;Regression;Stochasticprocess.1.INTRODUCTIONLikelihoodiscentraltomuchtheoreticaldiscussionofstatisticalinference,fromwhat-everviewpoint.Insimplecases,thelikelihoodisjustthejointdensityoftheobservedvaluesconsideredasafunctio
6、noftheunknownparameters.Theintroductionofmodifieddefini-tionsforcomplicatedproblemsisduetoBartlett(1937),notablerecentcontributionsbeingbyFraser(1968),Kalbfleisch&Sprott(1970),andAndersen(1973).Possibleaimsofmodifiedlikelihoodfunctionsinclude:(i)theachievementofrobustness;(ii)thestudyofprobl
7、ems,especiallyinstochasticprocesses,forwhichthefulllikelihoodisdifficultorimpossibletocompute;(iii)theneedtodevelopmethodsbasedonsecond-momentpropertiesratherthanfulldistributionalassumptions(Wedderburn,1974);(iv)thereductionofdimensionalityinsitua
