Asymptotic Normality of the Kernel Quantile Estimator

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.

Asymptotic Normality of U -Quantile-Statistics

In 1948, W. Hoeffding introduced a large class of unbiased estimators called U -statistics, defined as the average value of a real-valued m-variate function h calculated at all possible sets of m points from a random sample. In the present paper, we investigate the corresponding robust analogue which we call U -quantile-statistics. We are concerned with the asymptotic behavior of the sample p-q...

Asymptotic Normality of a Nonparametric Conditional Quantile Estimator for Random Fields

Asymptotic normality of the deconvolution kernel density estimator under the vanishing error variance

Let X1, . . . , Xn be i.i.d. observations, whereXi = Yi+σnZi and the Y ’s and Z’s are independent. Assume that the Y ’s are unobservable and that they have the density f and also that the Z’s have a known density k. Furthermore, let σn depend on n and let σn → 0 as n → ∞. We consider the deconvolution problem, i.e. the problem of estimation of the density f based on the sample X1, . . . , Xn. A...

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...