Asymptotic Normality of a Nonparametric Conditional Quantile Estimator for Random Fields

Asymptotic Normality of a Nonparametric Conditional Quantile Estimator for Random Fields

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 a nonparametric estimator of sample coverage

This paper establishes a necessary and sufficient condition for the asymptotic normality of the nonparametric estimator of sample coverage proposed by Good [Biometrica 40 (1953) 237–264]. This new necessary and sufficient condition extends the validity of the asymptotic normality beyond the previously proven cases.

Asymptotic Normality of Kernel Type Density Estimators for Random Fields

Kernel type density estimators are studied for random fields. It is proved that the estimators are asymptotically normal if the set of locations of observations become more and more dense in an increasing sequence of domains. It turns out that in our setting the covariance structure of the limiting normal distribution can be a combination of those of the continuous parameter and the discrete pa...

Asymptotic normality for deconvolution kernel density estimators from random fields

The paper discusses the estimation of a continuous density function of the target random field Xi, i ∈ Z N which is contaminated by measurement errors. In particular, the observed random field Yi, i ∈ Z N is such that Yi = Xi + ǫi, where the random error ǫi is from a known distribution and independent of the target random field. Compared to the existing results, the paper is improved in two dir...