Open Access
May 2010 Conditional density estimation in a censored single-index regression model
Olivier Bouaziz, Olivier Lopez
Bernoulli 16(2): 514-542 (May 2010). DOI: 10.3150/09-BEJ221


Under a single-index regression assumption, we introduce a new semiparametric procedure to estimate a conditional density of a censored response. The regression model can be seen as a generalization of the Cox regression model and also as a profitable tool for performing dimension reduction under censoring. This technique extends the results of Delecroix et al. [J. Multivariate Anal. 86 (2003) 213–226]. We derive consistency and asymptotic normality of our estimator of the index parameter by proving its asymptotic equivalence with the (uncomputable) maximum likelihood estimator, using martingales results for counting processes and arguments from empirical processes theory. Furthermore, we provide a new adaptive procedure which allows us both to choose the smoothing parameter involved in our approach and to circumvent the weak performances of the Kaplan–Meier estimator [Amer. Statist. Assoc. 53 (1958) 457–481] in the right-tail of the distribution. By means of a simulation study, we study the behavior of our estimator for small samples.


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Olivier Bouaziz. Olivier Lopez. "Conditional density estimation in a censored single-index regression model." Bernoulli 16 (2) 514 - 542, May 2010.


Published: May 2010
First available in Project Euclid: 25 May 2010

zbMATH: 1323.62095
MathSciNet: MR2668913
Digital Object Identifier: 10.3150/09-BEJ221

Keywords: asymptotic normality , Censoring , Empirical processes , martingales for counting processes , pseudo-maximum likelihood , Single-index model

Rights: Copyright © 2010 Bernoulli Society for Mathematical Statistics and Probability

Vol.16 • No. 2 • May 2010
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