An Asymptotically Optimal Adaptive Selection Procedure in the Proportional Hazards Model with Conditionally Independent Censoring

摘要

Assume k independent populations are given which are distributed according to R_(v_1), …, R_(v_k) (v_i ∈ Θ is contained in R). Taking samples of size n the population with the smallest v-value is to be selected. Using the framework of Le Cam's decision theory (Le Cam, 1986; Strasser, 1985) under mild regularity assumptions, an asymptotically optimal selection procedure is derived for the sequence of localized models. In the proportional hazards model with conditionally independent censoring, an asymptotically optimal adaptive selection procedure is constructed by substituting the unknown nuisance parameter by a kernel estimator.