The Annals of Statistics

Nonparametric Estimation in the Cox Model

Finbarr O'Sullivan

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Nonparametric estimation of the relative risk in a generalized Cox model with multivariate time dependent covariates is considered. Estimation is based on a penalized partial likelihood. Using techniques from Andersen and Gill, and Cox and O'Sullivan, upper bounds on rate of convergence in a variety of norms are obtained. These upper bounds match the optimal rates available for linear nonparametric regression and density estimation. The results are uniform in the smoothing parameter, which is an important step for the analysis of data dependent rules for the selection of the smoothing parameter.

Article information

Ann. Statist., Volume 21, Number 1 (1993), 124-145.

First available in Project Euclid: 12 April 2007

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Zentralblatt MATH identifier


Primary: 62G05: Estimation
Secondary: 62P10: Applications to biology and medical sciences 41A35: Approximation by operators (in particular, by integral operators) 41A25: Rate of convergence, degree of approximation 47A53: (Semi-) Fredholm operators; index theories [See also 58B15, 58J20] 45L10 45M05: Asymptotics

Cox model martingales penalized partial likelihood rates of convergence relative risk


O'Sullivan, Finbarr. Nonparametric Estimation in the Cox Model. Ann. Statist. 21 (1993), no. 1, 124--145. doi:10.1214/aos/1176349018.

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