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August 2000 Functional ANOVA modeling for proportional hazards regression
Jianhua Z. Huang, Charles Kooperberg, Charles J. Stone, Young K. Truong
Ann. Statist. 28(4): 961-999 (August 2000). DOI: 10.1214/aos/1015956704


The logarithm of the relative risk function in a proportional hazards model involving one or more possibly time-dependent covariates is treated as a specified sum of a constant term, main effects, and selected interaction terms. Maximum partial likelihood estimation is used, where the maximization is taken over a suitably chosen finite-dimensional estimation space, whose dimension increases with the sample size and which is constructed from linear spaces of functions of one covariate and their tensor products. The $L_2$ rate of convergence for the estimate and its ANOVA components is obtained. An adaptive numerical implementation is discussed, whose performance is compared to (full likelihood) hazard regression both with and without the restriction to proportional hazards.


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Jianhua Z. Huang. Charles Kooperberg. Charles J. Stone. Young K. Truong. "Functional ANOVA modeling for proportional hazards regression." Ann. Statist. 28 (4) 961 - 999, August 2000.


Published: August 2000
First available in Project Euclid: 12 March 2002

zbMATH: 1105.62378
MathSciNet: MR1810916
Digital Object Identifier: 10.1214/aos/1015956704

Primary: 62N05
Secondary: 62G05

Keywords: Convergence rates , Cox model , partial likelihood , splines , tensor product

Rights: Copyright © 2000 Institute of Mathematical Statistics


Vol.28 • No. 4 • August 2000
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