Asymptotic properties of a conditional quantile estimator with randomly truncated data

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.

Asymptotic Behaviors of Nearest Neighbor Kernel Density Estimator in Left-truncated Data

Kernel density estimators are the basic tools for density estimation in non-parametric statistics.  The k-nearest neighbor kernel estimators represent a special form of kernel density estimators, in  which  the  bandwidth  is varied depending on the location of the sample points. In this paper‎, we  initially introduce the k-nearest neighbor kernel density estimator in the random left-truncatio...

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...

Asymptotic normality of Hill Estimator for truncated data

The problem of estimating the tail index from truncated data is addressed in ?. In that paper, a sample based (and hence random) choice of k is suggested, and it is shown that the choice leads to a consistent estimator of the inverse of the tail index. In this paper, the second order behavior of the Hill estimator with that choice of k is studied, under some additional assumptions. In the untru...

Asymptotic Normality of a Nonparametric Conditional Quantile Estimator for Random Fields