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Smoothed Cox regression. (English) Zbl 0936.62046
Summary: Nonparametric regression was shown by R. Beran [Nonparametric regression with randomly censored survival data. Tech. Rep. Univ. California, Berkeley (1981)] and I. W. McKeague and K. J. Utikal [Ann. Stat. 18, No. 3, 1172-1187 (1990; Zbl 0721.62087); Scand. J. Stat. 18, No. 3, 177-195 (1991; Zbl 0803.62038)] to provide a flexible method for analysis of censored failure times and more general counting processes models in the presence of covariates. We discuss application of kernel smoothing towards estimation in a generalized Cox regression model with baseline intensity dependent on a covariate. Under regularity conditions we show that estimates of the regression parameters are asymptotically normal at rate root-\(n\), and we also discuss estimation of the baseline cumulative hazard function and related parameters.

MSC:
62G08 Nonparametric regression and quantile regression
62M09 Non-Markovian processes: estimation
62G20 Asymptotic properties of nonparametric inference
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