Zucker, David M.; Karr, Alan F. Nonparametric survival analysis with time-dependent covariate effects: A penalized partial likelihood approach. (English) Zbl 0708.62035 Ann. Stat. 18, No. 1, 329-353 (1990). The goal of this paper is the estimation of the regression function \(\beta_ 0\) in a (generalized) Cox model, in which the hazard function has the representation \[ \lambda (t| z)=\lambda_ 0(t)\exp [\sum^{p}_{j=1}\beta_{oj}(t)z_ j]. \] The estimator results from maximization of an appropriate penalized partial likelihood. Consistency and (pointwise) asymptotic normality are shown. Proofs use methods from Sobolev-spaces and martingale theory. Reviewer: W.Stute Cited in 3 ReviewsCited in 67 Documents MSC: 62G07 Density estimation 62G20 Asymptotic properties of nonparametric inference 62J02 General nonlinear regression Keywords:penalized maximum likelihood estimation; nonparametric regression; Cox model; hazard function; penalized partial likelihood; Consistency; asymptotic normality; Sobolev-spaces; martingale theory PDFBibTeX XMLCite \textit{D. M. Zucker} and \textit{A. F. Karr}, Ann. Stat. 18, No. 1, 329--353 (1990; Zbl 0708.62035) Full Text: DOI