Uniform representation of product-limit integrals with applications
(2004) , 23 pages
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- 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. A bootstrap approximation is proposed to approximate the distribution of the product-limit integrals.
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Citations
Sánchez Sellero, C., González Manteiga, W., & Van Keilegom, I. (2004). Uniform representation of product-limit integrals with applications (STAT Discussion Papers 0404). https://hdl.handle.net/2078.5/160900