• Bernoulli
  • Volume 16, Number 2 (2010), 514-542.

Conditional density estimation in a censored single-index regression model

Olivier Bouaziz and Olivier Lopez

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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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Bernoulli, Volume 16, Number 2 (2010), 514-542.

First available in Project Euclid: 25 May 2010

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asymptotic normality censoring empirical processes martingales for counting processes pseudo-maximum likelihood single-index model


Bouaziz, Olivier; Lopez, Olivier. Conditional density estimation in a censored single-index regression model. Bernoulli 16 (2010), no. 2, 514--542. doi:10.3150/09-BEJ221.

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