Premium
An Asymptotically Optimal Adaptive Selection Procedure in the Proportional Hazards Model with Conditionally Independent Censoring
Author(s) -
Wienke Andreas
Publication year - 1998
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/(sici)1521-4036(199812)40:8<963::aid-bimj963>3.0.co;2-4
Subject(s) - mathematics , asymptotically optimal algorithm , censoring (clinical trials) , estimator , statistics , selection (genetic algorithm) , population , kernel (algebra) , mathematical optimization , combinatorics , computer science , demography , artificial intelligence , sociology
Assume k independent populations are given which are distributed according to R ϑ 1, …, R ϑ k(ϑ i ∈ Θ ⊆ R ). Taking samples of size n the population with the smallest ϑ‐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.