Construction of Asymptotically Optimal and Independent Nonparametric ExperimentalDesign Tests in the Cox Regression Model and for Distributions with a Location Parameter

摘要

Considered is the Cox-regression-model lambda(t;beta,Z)=lambda(t)exp(beta'Z), inwhich Z is the indication-vector with respect to k life-time distributions and beta the regression-vector; the basic failure rate lambda(t) is unknown. It is assumed that from each population n objects are observed during (0,1), all life-times being independently distributed, while balanced censoring during (0,1) is allowed. For sequences (beta sub n) with n(sub 1/2)beta(sub n) -> beta two asymptotically optimal and equivalent tests are derived for the hypothesis H(sub 0): n(sup 1/2)A(beta(sub n)) -> d, in which A is a contrast matrix, against the alternative H(sub 1): n(sup 1/2)A(beta (sub n)) not -> d).