Results on standard estimators in the Cox model

2019/08/20 by Cécile Durot, Durot, Cécile, Eni Musta +1
Economics, Econometrics and Finance · Mathematics · #Advanced Statistical Methods and Models #FOS: Mathematics #Financial Risk and Volatility Modeling #Statistical Methods and Inference #Statistics Theory (math.ST) #math.ST #stat.TH

paper · pdf · doi:10.48550/arxiv.1908.07456

openalex publication_date 2019/08/20 · openalex created_date 2019/08/29 · arxiv created 2020/02/19 · arxiv updated 2020/02/20 · openalex updated_date 2026/07/28

Abstract

We consider the Cox regression model and prove some properties of the maximum partial likelihood estimator β_n and of the the Breslow estimator Λ_n. The asymptotic properties of these estimators have been widely studied in the literature but we are not aware of a reference where it is shown that they have uniformly bounded moments. These results are needed, for example, when studying global errors of shape restricted estimators of the baseline hazard function.

Citations

• Cox's Regression Model for Counting Processes: A Large Sample Study
• On the L_p-error of the Grenander-type estimator in the Cox model

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