In this paper we analyze the world´s cross-national distribution of income and its evolution from 1970 to 2003. We argue that modeling this distribution by a finite mixture and investigating its number of components has advantages over nonparametric inference concerning the number of modes. In...

The problem of estimating an unknown density function has been widely studied. In this paper we present a convolution estimator for the density of the responses in a nonlinear regression model. The rate of convergence for the variance of the convolution estimator is of order 1/n. This is faster...

The Gaussian kernel density estimator is known to have substantial problems for bounded random variables with high density at the boundaries. For i.i.d. data several solutions have been put forward to solve this boundary problem. In this paper we propose the gamma kernel estimator as density...

The Gaussian kernel density estimator is known to have substantial problems for bounded random variables with high density at the boundaries. For i.i.d. data several solutions have been put forward to solve this boundary problem. In this paper we propose the gamma kernel estimator as density...

Simple kernel-type estimators of integrals of general powers of general derivatives of probability densities are proposed. They are based on two simple properties, and in many circumstances enjoy optimal convergence rate.

This paper establishes the asymptotic normality of frequency polygons in the context of stationary strongly mixing random fields indexed by <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$\mathbb {Z}^d$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <msup> <mrow> <mi mathvariant="double-struck">Z</mi> </mrow> <mi>d</mi> </msup> </math> </EquationSource> </InlineEquation>. Our method allows us to consider only minimal conditions on the width bins and provides a simple criterion on the mixing...</equationsource></equationsource></inlineequation>

We present a sharp uniform-in-bandwidth limit law for the nearest-neighbor density estimator. Our result is established in the framework of convergence in probability, and we allow the bandwidth to vary within the complete range for which the estimator is consistent. We provide the explicit...

Motivated by the optimality condition of a quantile loss minimization problem, a new family of closed-form density estimators based on truncated means is developed and found to achieve smaller mean squared errors in estimating the tails of the normal and gamma distributions when compared to the...

In this paper, we consider the non-parametric, kernel estimate of the density, f(x), for data drawn from stratified samples. Much of the data used by social scientists is gathered in some type of complex survey violating the usual assumptions of independently and identically distributed data....