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Uniform Representation of Product-Limit Integrals with Applications
Authors:CÉ  SAR SÁ  NCHEZ SELLERO,WENCESLAO GONZÁ  LEZ MANTEIGA, INGRID,VAN,KEILEGOM
Affiliation:Departamento de Estadística e I.O., Universidad de Santiago de Compostela; Institut de Statistique, Universitécatholique de Louvain
Abstract:Abstract.  Let X be a d -variate random vector that is completely observed, and let Y be a random variable that is subject to right censoring and left truncation. For arbitrary functions φ we consider expectations of the form E [ φ ( X ,  Y )], which appear in many statistical problems, and we estimate these expectations by using a product-limit estimator for censored and truncated data, extended to the context where covariates are present. An almost sure representation for these estimators is obtained, with a remainder term that is of a certain negligible order, uniformly over a class of φ -functions. This uniformity is important for the application to goodness-of-fit testing in regression and to inference for the regression depth, which we consider in more detail.
Keywords:censoring    goodness-of-fit    non-parametric regression    product-limit estimator    regression depth    truncation
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