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Activity Number: 637 - Non-Standard Regression Models
Type: Invited
Date/Time: Thursday, August 3, 2017 : 10:30 AM to 12:20 PM
Sponsor: IMS
Abstract #322103 View Presentation
Title: Global error of smooth estimators for a monotone baseline hazard in the Cox model
Author(s): Rik Lopuhaa* and Eni Musta
Companies: Delft University of Technology and Delft University of Technology
Keywords: smooth isotonic estimation ; global distances ; asymptotics ; Grenander estimator

Shape constrained nonparametric estimation dates back to the 1950s. In his milestone paper in 1956, Grenander derived the maximum likelihood estimator of a nonincreasing density, whereas Brunk (1958) obtained the least squares estimator of a monotone regression function. The last decades, similar estimators have been proposed in other statistical models, including Cox's proportional hazards model with a monotone baseline hazard. Typically, these isotonic estimators are step functions that exhibit a non normal limit distribution at cube-root n rate. On the other hand, a long stream of research has shown that, if one is willing to assume more regularity on the function of interest, smooth estimators can be used to achieve a faster rate of convergence to a Gaussian distributional law and to estimate derivatives. The asymptotic behavior of global distances between the estimator and the function of interest, such as L_p distances and supremum distance, has been studied for traditional isotonic estimators. In this talk, similar results are presented for smooth isotonic methods, e.g., right-censored data.

Authors who are presenting talks have a * after their name.

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