Single-index Regression models with right-censored responses

TL;DR

This paper introduces new estimation methods for single-index regression models with right-censored responses, establishing their consistency and asymptotic properties, and compares them with existing techniques through simulations.

Contribution

It generalizes M-estimation procedures for censored data, providing theoretical guarantees and practical comparisons with prior methods.

Findings

Estimates are consistent and asymptotically normal.

New estimators perform well compared to existing methods.

Simulation results validate theoretical properties.

Abstract

In this article, we propose some new generalizations of M-estimation procedures for single-index regression models in presence of randomly right-censored responses. We derive consistency and asymptotic normality of our estimates. The results are proved in order to be adapted to a wide range of techniques used in a censored regression framework (e.g. synthetic data or weighted least squares). As in the uncensored case, the estimator of the single-index parameter is seen to have the same asymptotic behavior as in a fully parametric scheme. We compare these new estimators with those based on the average derivative technique of Burke and Lu (2005) through a simulation study.