Conditional density estimation in a censored single-index regression model

TL;DR

This paper introduces a new semiparametric method for estimating the conditional density in a censored single-index regression model, extending Cox regression and improving dimension reduction under censoring.

Contribution

It develops a novel estimator with proven consistency and asymptotic normality, along with an adaptive procedure for smoothing parameter selection and tail performance enhancement.

Findings

Estimator shows good performance in small samples

Method effectively handles right-censored data

Improves tail estimation over Kaplan-Meier

Abstract

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 Cox regression model and also as a profitable tool to perform dimension reduction under censoring. This technique extends the results of Delecroix et al. (2003). 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 of empirical processes theory. Furthermore, we provide a new adaptive procedure which allows us both to chose the smoothing parameter involved in our approach and to circumvent the weak performances of Kaplan-Meier estimator (1958) in the right-tail of the distribution. Through a simulation study, we study the behavior of our estimator for small samples.