A Kernel Estimator of a Conditional Quantile

A Smooth Nonparametric Conditional Quantile Frontier Estimator

Traditional estimators for nonparametric frontier models (DEA, FDH) are very sensitive to extreme values/outliers. Recently, Aragon, Daouia, and Thomas-Agnan (2005) proposed a nonparametric α-frontier model and estimator based on a suitably defined conditional quantile which is more robust to extreme values/outliers. Their estimator is based on a nonsmooth empirical conditional distribution. In...

Kernel and Nearest Neighbor Estimation of a Conditional Quantile

Let (Xl'Z1)' (X2,Z2),· .. ,(Xn,Zn) be LLd. as (X,Z), Z taking values in Rl, and for o < p < 1, let ep(x) denote the conditional p-quantile of Z given X=x, i.e., P(Z ~ ep(x) IX=x) = p. In this paper, kernel and nearest neighbor estimators of ep(x) are proposed. As a first step in studying the asymptotics of these estimates, Bahadur type ~ representations of the sample conditional quantile functi...

Asymptotic Normality of a Nonparametric Conditional Quantile Estimator for Random Fields

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.

A Berry-Esseen Type Bound for the Kernel Density Estimator of Length-Biased Data

Length-biased data are widely seen in applications. They are mostly applicable in epidemiological studies or survival analysis in medical researches. Here we aim to propose a Berry-Esseen type bound for the kernel density estimator of this kind of data.The rate of normal convergence in the proposed Berry-Esseen type theorem is shown to be O(n^(-1/6) ) modulo logarithmic term as n tends to infin...