Asymptotic Normality of an M-estimator of regression function for truncated-censored data under alpha-mixing condition

TL;DR

This paper proves the asymptotic normality of an M-estimator for regression functions in truncated-censored data under alpha-mixing conditions, extending classical results to dependent data and unbounded objective functions.

Contribution

It establishes weak consistency and asymptotic normality of the M-estimator in LTRC models with dependent data, including kernel regression and distribution estimators.

Findings

M-estimator is asymptotically normal under alpha-mixing.

Uniform convergence rate for product-limit estimator under dependence.

Simulation results support theoretical findings.

Abstract

In this paper, we establish weak consistency and asymptotic normality of an M-estimator of the regression function for left truncated and right censored (LTRC) model, where it is assumed that the observations form a stationary alpha-mixing sequence. The result holds with unbounded objective function, and are applied to derive weak consistency and asymptotic normality of a kernel classical regression curve estimate. We also obtain a uniform weak convergence rate for the product-limit estimator of the lifetime and censored distribution under dependence, which are useful results for our study and other LTRC strong mixing framework. Some simulations are drawn to illustrate the results for finite sample.