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On the Lp error of the Grenander‐type estimator in the Cox model

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  • Cécile Durot
  • Eni Musta

Abstract

We consider the Cox regression model and study the asymptotic global behavior of the Grenander‐type estimator for a monotone baseline hazard function. This model is not included in the general setting of Durot (2007). However, we show that a similar central limit theorem holds for Lp‐error of the Grenander‐type estimator. As an illustration of application of our main result, we propose a test procedure for a Weibull baseline distribution, based on the Lp‐distance between the Grenander estimator and a parametric estimator of the baseline hazard. Simulation studies are performed to investigate the performance of this test.

Suggested Citation

  • Cécile Durot & Eni Musta, 2020. "On the Lp error of the Grenander‐type estimator in the Cox model," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 74(4), pages 559-591, November.
    • Handle: RePEc:bla:stanee:v:74:y:2020:i:4:p:559-591
    DOI: 10.1111/stan.12218
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    References listed on IDEAS

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    1. Chung, Daehyun & Chang, Myron N., 1994. "An isotonic estimator of the baseline hazard function in Cox's regression model under order restriction," Statistics & Probability Letters, Elsevier, vol. 21(3), pages 223-228, October.
    2. Hendrik P. Lopuhaä & Eni Musta, 2018. "Smoothed Isotonic Estimators of a Monotone Baseline Hazard in the Cox Model," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 45(3), pages 753-791, September.
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