Censored quantile regression processes under dependence and penalization

TL;DR

This paper develops new methods for censored quantile regression processes that handle dependent data and high-dimensional parameters, introducing novel penalization techniques with optimal convergence rates.

Contribution

It introduces new penalization methods for censored quantile regression that outperform traditional estimators, especially under dependence and high-dimensional settings.

Findings

Derived a uniform Bahadur representation for censored quantile processes.

Proposed penalization techniques achieving optimal convergence rates.

Handled dependent data without requiring independence assumptions.

Abstract

We consider quantile regression processes from censored data under dependent data structures and derive a uniform Bahadur representation for those processes. We also consider cases where the dimension of the parameter in the quantile regression model is large. It is demonstrated that traditional penalized estimators such as the adaptive lasso yield sub-optimal rates if the coefficients of the quantile regression cross zero. New penalization techniques are introduced which are able to deal with specific problems of censored data and yield estimates with an optimal rate. In contrast to most of the literature, the asymptotic analysis does not require the assumption of independent observations, but is based on rather weak assumptions, which are satisfied for many kinds of dependent data.