Comparative Analysis of Robust Reduction of a Multidimensional Economic Indicators

This research work considers the application of the principal component analysis for cases when distributions are heavy-tailed, and the outliers are presented. The aim of the study is to make modification of the principal component analysis (PCA) based on robust estimates of correlation matrixes. It is proposed to use the Spearman coefficient, the MADN estimate and the MCD estimate instead of using the sample Pearson correlation coefficient, while calculating loading matrixes. Main results of modelling in this work show that for heavy-tailed distributions with outliers it is preferred to use robust estimates rather than the classical approach of the PCA. For real economic data analysis robust adaptation versions of the PCA were successfully applied. Robust estimates were effective for profitability of ten companies from three different spheres. It allowed to extract three principal components both for real data and data with artificially created outliers.