POLYNOMIAL ESTIMATION OF DATA MODEL PARAMETERS WITH NEGATIVE KURTOSIS

Abstract

Context. The paper focuses on the problem of estimating the center of distribution of the random component of experimental data for density models with a negative kurtosis.
 Objective. The goal of this research is to develop methods to improve the efficiency of polynomial estimation of parameters of experimental data with a negative kurtosis coefficient.
 Method. The study applies a relatively new approach to obtaining estimates for the center of the probability distribution from the results of experimental data with a stochastic component. This approach is based on polynomial estimation methods that rely on the mathematical apparatus of Kunchenko's stochastic polynomials and the description of random variables by higher-order statistics (moments or cumulants). A number of probability density distributions with a negative kurtosis coefficient are used as models of the random component.
 As a measure of efficiency, the ratio of variance of the estimates for the center of the distribution found using polynomial and classical methods based on the parameter of amount of information obtained is used.
 The relative accuracy of polynomial estimates in comparison with the estimates of the mean, median and quantile estimates (center of curvature) is researched using the Monte Carlo method for multiple tests.
 Results. Polynomial methods for estimating the distribution center parameter for data models of probability distribution density with a negative kurtosis coefficient have been constructed.
 Conclusions. The research carried out in this paper confirms the potentially high efficiency of polynomial estimates of the coordinates of the center of the experimental data, which are adequately described by model distributions with a negative kurtosis. Statistical modeling has confirmed the effectiveness of the obtained estimates in comparison with the known non-parametric estimates based on the statistics of the mean, median, and quantile, even with small sample sizes.