NONPARAMETRIC-ESTIMATION IN THE COX MODEL

• 成果类型: Article
• 署名作者: OSULLIVAN, F
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176349018
• 发表日期: 1993
• 页码: 124-145
• 关键词: regression-model; Cross-validation; spline functions; likelihood

摘要

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 ruler, for the selection of the smoothing parameter.