Open Access
July 2007 Inference under right censoring for transformation models with a change-point based on a covariate threshold
Michael R. Kosorok, Rui Song
Ann. Statist. 35(3): 957-989 (July 2007). DOI: 10.1214/009053606000001244


We consider linear transformation models applied to right censored survival data with a change-point in the regression coefficient based on a covariate threshold. We establish consistency and weak convergence of the nonparametric maximum likelihood estimators. The change-point parameter is shown to be n-consistent, while the remaining parameters are shown to have the expected root-n consistency. We show that the procedure is adaptive in the sense that the nonthreshold parameters are estimable with the same precision as if the true threshold value were known. We also develop Monte Carlo methods of inference for model parameters and score tests for the existence of a change-point. A key difficulty here is that some of the model parameters are not identifiable under the null hypothesis of no change-point. Simulation studies establish the validity of the proposed score tests for finite sample sizes.


Download Citation

Michael R. Kosorok. Rui Song. "Inference under right censoring for transformation models with a change-point based on a covariate threshold." Ann. Statist. 35 (3) 957 - 989, July 2007.


Published: July 2007
First available in Project Euclid: 24 July 2007

zbMATH: 1136.62376
MathSciNet: MR2341694
Digital Object Identifier: 10.1214/009053606000001244

Primary: 62F05 , 62N01
Secondary: 62G10 , 62G20

Keywords: Change-point models , Empirical processes , Nonparametric maximum likelihood , proportional hazards model , proportional odds model , right censoring , Semiparametric efficiency , Transformation models

Rights: Copyright © 2007 Institute of Mathematical Statistics

Vol.35 • No. 3 • July 2007
Back to Top