On a semiparametric survival model with flexible covariate effect
type: Item
instance of: scholarly article
title: On a semiparametric survival model with flexible covariate effect
zbMATH Open document ID: 0953.62107
published in: The Annals of Statistics
publication date: 1999-11-09T00:00:00Z
review text: The Cox regression model specifies the stochastic hazard rate at exposure time \(t\) for covariate \(z\) as \[ \lambda(z,t)= \alpha(t) \exp(\beta z), \tag{1} \] where \(\alpha\) is nonparametric while the dependency on the marker or covariate \(z\) is parametric. The authors suppose \[ \lambda(z,t)= \alpha(t; \theta)g(z), \tag{2} \] where \(\alpha\) is a parametric class of hazard functions, while \(g\) is of unknown functional form. In Section 2 are presented the counting process formulation of the model, while in Section 3 are defined estimators of \(\theta\) and \(g\) in (2), based on the profile likelihood principle. In Section 4 are considered the asymptotic properties of the parametric and nonparametric estimates outlining the general approach to the asymptotics. Section 5 contains numerical results and some extensions are discussed in Section 6. The proofs are given in the Appendix. All the sections contain a rich and impressive bibliography.
Mathematics Subject Classification ID: 62N02
Mathematics Subject Classification ID: 62M09
Mathematics Subject Classification ID: 62G05
Mathematics Subject Classification ID: 62F12
Mathematics Subject Classification ID: 62G20
zbMATH DE Number: 1359513
zbMATH Keywords: counting processes
zbMATH Keywords: kernel estimation
zbMATH Keywords: predictability
zbMATH Keywords: semiparametric survival analysis
zbMATH Keywords: bibliography
author: P. J. Bickel
author: Jens Perch Nielsen
author: Oliver Linton
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aos/1030563983
OpenAlex ID: W1964333077
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DOI: 10.1214/AOS/1030563983
description: scientific article; zbMATH DE number 1359513