| Abstract [eng] |
Density distribution is one of the most important features characterizing a random variable, therefore its estimation is very important. In this paper nonparametric statistical estimation of multivariate probability density is presented. For that purpose, the model of projection pursuit density estimation (PPDE) was chosen. The projection pursuit density estimation idea was proposed by J. H. Friedman (1974). The author suggests these PPDE parts: 1) Find all interesting univariate projections. The more projection’s univariate density differs from standard Gaussian density, the more interesting it is; 2) Apply a transformation to the data which removes the structure in the found projection direction, so that its projection has standard Gaussian density; 3) Estimate multivariate probability density of the data using the found interesting projection directions. The main purpose of this work is multivariate probability density estimation using projection pursuit density estimation method. The main tasks: • Analysis of Projection pursuit density estimator with different data samples; • Analysis of Projection pursuit density estimator using Mardia‘s skewness and kurtosis, Henze – Zirkler, Royston H tests for normality; Findings and recommendations for approaches which produce the smallest errors for samples of small and large sizes are presented in the conclusions section. |
