Theory of Probability and Mathematical Statistics
Goodness-of-fit test in Cox proportional hazards model with measurement errors
A. G. Kukush, O. O. Chernova
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Abstract: Cox proportional hazards model with measurement errors is studied, in which baseline hazard rate λ(·) belongs to a parameter set consisting of nonnegative Lipschitz functions, with fixed constant, and regression parameter β belongs to a compact parameter set. Censored lifetime and regressors with additive errors are observed. We construct a goodness-of-fit test based of strongly consistent simultaneous estimator for λ(·) and β derived in parer of Kukush and Chernova (2017) [6]. The test statistic is asymptotically chi-squared under null hypothesis. The power of the test under local alternatives is evaluated.
Keywords: Consistent estimator, goodness-of-fit test, local alternatives, Cox proportional hazards model, power of test, simultaneous estimator of baseline hazard rate and regression parameter.
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