Asymptotic normality of the Parzen–Rosenblatt density estimator for strongly mixing random fields

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...

Asymptotic Normality of a Nonparametric Conditional Quantile Estimator for Random Fields

Asymptotic normality of Powell’s kernel estimator

In this paper, we establish asymptotic normality of Powell’s kernel estimator for the asymptotic covariance matrix of the quantile regression estimator for both i.i.d. and weakly dependent data. As an application, we derive the optimal bandwidth that minimizes the approximate mean squared error of the kernel estimator.

Best Asymptotic Normality of the Kernel Density Entropy Estimator for Smooth Densities

In the random sampling setting we estimate the entropy of a probability density distribution by the entropy of a kernel density estimator using the double exponential kernel. Under mild smoothness and moment conditions we show that the entropy of the kernel density estimator equals a sum of independent and identically distributed (i.i.d.) random variables plus a perturbation which is asymptotic...