Isotonic Window Estimators of the Baseline Hazard Function in Cox's Regression Model Under Order Restriction

• Published in: Scandinavian journal of statistics Vol. 25; no. 1; pp. 151 - 161
• Main Authors: Chang, Myron N., Chung, Daehyun
• Format: Journal Article
• Language: English
• Published: Oxford, UK and Boston, USA Blackwell Publishers Ltd 01.03.1998; Blackwell Publishers; Blackwell
• Subjects: asymptotic normality; Censorship; convergence rate; Density estimation; empirical estimator; Estimators; Exact sciences and technology; Gaussian distributions; Increasing functions; Inference from stochastic processes; time series analysis; isotonic regression; Linear inference, regression; Mathematical functions; Mathematics; Maximum likelihood estimation; maximum likelihood estimator; maximum partial likelihood estimator; mean square error; Probability and statistics; Regression analysis; Sciences and techniques of general use; Statistical inferences; Statistics; weighted least-squares cross-validation; Order restriction; Cox model; Empirical process; Regression model; Asymptotic normality; Bandwith selection; Convergence rate; Cross validation; Maximum likelihood; Mean square error
• ISSN: 0303-6898; 1467-9469
• DOI: 10.1111/1467-9469.00095

The regression model suggested by Cox (1972) has been widely used in survival analysis with censored observations. We propose isotonic window estimators for a monotone baseline hazard function in the Cox regression model. We prove that these estimators are asymptotically normal. The simulation results presented in the article suggest that the proposed estimator performs better than several existing estimators in the literature.