Nonparametric Likelihood Ratio Estimation of Probabilities for Truncated Data

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Gang Li
We considert he problemo f intervale stimationo f probabilitiefso r randomlyt runcatedd ata.T he best-knownm ethodi s basedo n
the normala pproximationof the product-limiet stimatora nd has a drawbackth at it may producei ntervalsc ontainingi mpossible
valueso utsidet he range[ 0, 1]. Its small-samplep erformanceis also not satisfactoryI.n this articlew e investigatea n alternative
approacht hat derivesc onfidencei ntervalsd irectlyf rom a conditionaln onparametrilci kelihoodr atio. The method is an exact
nonparametriacn alogo f the classicalp arametricli kelihoodr atio theory,w ith the parameters pace now being the family of all
distributionsI.t hasa n appealingp ropertyth att he resultingc onfidencein tervalsa rea lwayss ubintervalosf [0, 1]. It alsod emonstrated
a betters mall-samplpe erformancien our simulations tudies.T hisa pproachis generalizedto obtainc onfidencein tervalsf ort he ratio
of two probabilitiesm, akej oint inferenceso n any finite numbero f probabilitiesa, nd test goodnesso f fit of a given distribution
function.T he small-samplpe erformanceosf threed ifferenmt ethodsa re investigatedin a MonteC arlos tudy.A n illustrationis also
givenu singt he Centersf or DiseaseC ontrol'st ransfusionr elateda cquiredim muned eficiencys yndromed ata.
KEY WORDS: Acquiredim muned eficiencys yndromeE; mpiricalli kelihoodG; oodnesso f fit; Humani mmunodeficiencvyi rus;
Incubationp eriod;I ntervale stimationP; roductl imit estimate;T runcation

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关键词：Likelihood Estimation Parametric Abilities truncated Data Estimation Likelihood ratio truncated

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