Nonparametric quantile regression for twice censored data

TL;DR

This paper introduces two novel nonparametric quantile regression methods for twice censored data, utilizing monotone rearrangements to prevent crossing quantile curves, with proven consistency and convergence properties.

Contribution

The paper proposes new estimates for twice censored data using monotone rearrangements, addressing the crossing quantile issue and establishing their theoretical properties.

Findings

Proposed methods are weakly consistent and converge weakly.

Simulation studies demonstrate finite sample performance.

New results on weak convergence of Beran estimator for right censored data.

Abstract

We consider the problem of nonparametric quantile regression for twice censored data. Two new estimates are presented, which are constructed by applying concepts of monotone rearrangements to estimates of the conditional distribution function. The proposed methods avoid the problem of crossing quantile curves. Weak uniform consistency and weak convergence is established for both estimates and their finite sample properties are investigated by means of a simulation study. As a by-product, we obtain a new result regarding the weak convergence of the Beran estimator for right censored data on the maximal possible domain, which is of its own interest.