Nonparametric M-estimation for right censored regression model with stationary ergodic data

TL;DR

This paper introduces a nonparametric M-estimator for right censored regression with stationary ergodic data, establishing its consistency, asymptotic properties, and providing a practical confidence interval without requiring mixing conditions or marginal densities.

Contribution

It develops a robust kernel-based estimator for right censored regression in stationary ergodic settings, with proven consistency and asymptotic distribution, and offers a confidence interval independent of unknown parameters.

Findings

Estimator is strongly consistent with a known rate.

Asymptotic distribution of the estimator is derived.

Confidence intervals are constructed without unknown quantities.

Abstract

The present paper deals with a nonparametric M-estimation for right censored regression model with stationary ergodic data. Defined as an implicit function, a kernel type estimator of a family of robust regression is considered when the covariate take its values in R^d (d >= 1) and the data are sampled from stationary ergodic process. The strong consistency (with rate) and the asymptotic distribution of the estimator are established under mild assumptions. Moreover, a usable confidence interval is provided which does not depend on any unknown quantity. Our results hold without any mixing condition and do not require the existence of marginal densities. A comparison study based on simulated data is also provided.