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Nonparametric model checks in censored regression. (English) Zbl 1018.62030
Summary: Let \({\mathcal M}\) be a parametric model for an unknown regression function \(m\). In order to check the validity of \({\mathcal M}\), i.e., to test for \(m\in {\mathcal M}\), it is known that optimal tests should be based on the empirical process of the regressors marked by the residuals. We extend the methodology to censored regression. The asymptotic distribution of the underlying marked empirical process is provided. The wild Bootstrap, appropriately modified to account for censorship, provides distributional approximations. The method is applied to simulated data sets as well as to the Stanford Heart Transplant Data.

MSC:
62G08 Nonparametric regression and quantile regression
62N03 Testing in survival analysis and censored data
62G20 Asymptotic properties of nonparametric inference
62G30 Order statistics; empirical distribution functions
62G09 Nonparametric statistical resampling methods
Keywords:
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