Sellero, CS
Manteiga, WG
Van Keilegom, Ingrid
[UCL]
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 phi we consider expectations of the form E[phi(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 phi-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.
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Bibliographic reference |
Sellero, CS ; Manteiga, WG ; Van Keilegom, Ingrid. Uniform representation of product-limit integrals with applications. In: Scandinavian Journal of Statistics : theory and applications, Vol. 32, no. 4, p. 563-581 (2005) |
Permanent URL |
http://hdl.handle.net/2078.1/38995 |