Parametr wygładzania w estymacji jądrowej funkcji gęstości dla zmiennych losowych w badaniach ekonomicznych
Smoothing Parameter in Kernel Density Estimation for Random Variables in Economic Researches

Author(s): Aleksandra Baszczyńska
Subject(s): Economy
Published by: Wydawnictwo Uniwersytetu Łódzkiego
Keywords: Random Variable; Density Function; Kernel Estimation; Smoothing Parameter; Kernel Function; Generalized Form of Harmonic Mean; Economic Application; estymacja jądrowa; funkcje jądra; parametr wygładzania; zmienne losowe
Summary/Abstract: Kernel density estimation is one of the basic procedures used in economic analyzes, because density function univocally defines a random variable. The book presents the methods of kernel estimation of the density function, with particular emphasis on the procedures for selecting the smoothing parameter. Using simulation methods, the properties of smoothing parameters determined by the discussed methods were analyzed, taking into account both the sample size and the form of the kernel function used in the kernel density function estimator. A new method of choosing a smoothing parameter based on the harmonic mean has also been proposed, which due to the generalized form of the mean is characterized by the universality in the use of this method. The examples of the application of the presented methods for selecting the smoothing parameter in the kernel estimation of the density function for random variables in economic researches are also presented.

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