Single index regression models with randomly left-truncated data

TL;DR

This paper introduces new generalized M-estimators for single index regression models with left-truncated data, demonstrating their consistency, asymptotic normality, and finite sample performance through simulations.

Contribution

It develops novel M-estimator procedures for single index models with left-truncated responses, extending existing kernel-based methods.

Findings

Establishes consistency and asymptotic normality of the estimators

Provides simulation results showing good finite sample performance

Extends kernel estimator methods to new regression settings

Abstract

In this paper, based on the kernel estimator proposed by Ould-Said and Lemdani (Ann. Instit. Statist. Math. 2006), we develop some new generalized M-estimator procedures for single index regression models with left-truncated responses. The consistency and asymptotic normality of our estimators are also established. Some simulation studies are given to investigate the finite sample performance of the proposed estimators.