Bahadur Representation of the Kernel Quantile Estimator under Random Censorship

A Note on the Smooth Estimator of the Quantile Function with Left-Truncated Data

This note focuses on estimating the quantile function based on the kernel smooth estimator under a truncated dependent model. The Bahadurtype representation of the kernel smooth estimator is established, and from the Bahadur representation it can be seen that this estimator is strongly consistent.

Bahadur Representation for the Nonparametric M-Estimator Under Alpha-mixing Dependence

Uniform bias study and Bahadur representation for local polynomial estimators of the conditional quantile function

This paper investigates the bias and the Bahadur representation of a local poly-nomial estimator of the conditional quantile function and its derivatives. Thebias and Bahadur remainder term are studied uniformly with respect to thequantile level, the covariates and the smoothing parameter. The order of thelocal polynomial estimator can be higher that the differentiability or...

The quantile process under random censoring

In this paper we discuss the asymptotical properties of quantile processes under random censoring. In contrast to most work in this area we prove weak convergence of an appropriately standardized quantile process under the assumption that the quantile regression model is only linear in the region, where the process is investigated. Additionally, we also discuss properties of the quantile proces...

Uniform Bahadur Representation for Nonparametric Censored Quantile Regression: A Redistribution-of-Mass Approach

Censored quantile regressions have received a great deal of attention in the literature. In a linear setup, recent research has found that an estimator based on the idea of “redistribution-of-mass” (Efron, 1967) has better numerical performance than other available methods. In this paper, this idea is combined with the local polynomial kernel smoothing for nonparametric quantile regression of c...