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Testing for a time dependent coefficient in Cox’s regression model. (English) Zbl 0782.62053
This paper considers the problem of testing time independence against time dependence of the coefficients of covariates in the Cox regression model. Since the class of alternatives is sufficiently wide the method of sieves is applied to the hypotheses testing problems. The test derived in this manner is shown to be consistent against a wide class of alternatives \(H_ n\) which approaches \(H_ 0\) at the rate of \(n\) to the power of \(-(3+\delta)/8\) where \(0<\delta<1\), and not of the usual rate of \(n\) to the power \(-1/2\).
Reviewer: B.K.Kale (Pune)

62G10 Nonparametric hypothesis testing
62F05 Asymptotic properties of parametric tests