We propose new procedures for estimating the component functions in both additive and multiplicative nonparametric marker-dependent hazard models. We work with a full counting process framework that allows for left truncation and right censoring and time-varying covariates. Our procedures are based on kernel hazard estimation as developed by Nielsen and Linton and on the idea of marginal integration. We provide a central limit theorem for the marginal integration estimator. We then define estimators based on finite-step backfitting in both additive and multiplicative cases and prove that these estimators are asymptotically normal and have smaller variance than the marginal integration method.
@article{1051027877,
author = {Linton, Oliver B. and Nielsen, Jens Perch and Van de Geer, Sara},
title = {Estimating multiplicative and additive hazard functions by kernel methods},
journal = {Ann. Statist.},
volume = {31},
number = {1},
year = {2003},
pages = { 464-492},
language = {en},
url = {http://dml.mathdoc.fr/item/1051027877}
}
Linton, Oliver B.; Nielsen, Jens Perch; Van de Geer, Sara. Estimating multiplicative and additive hazard functions by kernel methods. Ann. Statist., Tome 31 (2003) no. 1, pp. 464-492. http://gdmltest.u-ga.fr/item/1051027877/