METHOD OF ROBUST EVALUATION THAT USES CHEBYSHEV’S INEQUALITY, AND ITS APPLICATION TO ANALYSIS OF INCOMES IN RUSSIA

Abstract

The article describes implementation of the robust evaluation method, based on the Chebyshev’s inequality. Standard methods of estimation, including robust ones, that require knowledge about the type of the distribution function of the analyzed data are compared with the proposed distribution-free method provided. The emphasis is laid on the fact that if the goal is to extract maximum information from the sample of observations, a priori prediction about the type of the distribution function can lead to false conclusions, so distribution-free methods are required. The description of mathematical procedures of robust estimation method using Chebyshev’s inequality to calculate observations weights, is given. Comparison of location and scale estimations, provided by standard methods vs the proposed method, is made for univariate data. Computational experiments showed that in terms of robustness the proposed method is comparable to median estimation. As an application example, robust estimation method is applied to analysis of economic data about per capita income in Russia between 2001-2011 is considered.