Redukcja efektu brzegowego w estymacji jądrowej wybranych charakterystyk funkcyjnych zmiennej losowej

Abstract

For a random variable with bounded support, the kernel estimation of functional characteristics may lead to the occurrence of the so-called boundary effect. In the case of the kernel density estimation it can mean an increase of the estimator bias in the areas near the ends of the support, and can lead to a situation where the estimator is not a density function in the support of a random variable. In the paper the procedures for reducing boundary effect for kernel estimators of density function, distribution function and regression function are analyzed. Modifications of the classical kernel estimators and examples of applications of these procedures in the analysis of the functional characteristics relating to gross national product per capita are presented. The advantages of procedures are indicated taking into account the reduction of the bias in the boundary region of the support of the random variable considered.