Classical and Robust Correlation Estimates: A Comparative Study

Abstract

For conducting correlational analysis, one may be faced with statistical problem if the dataset contains outliers and other contaminations. In order to use any correlation method when the dataset contains outliers, one must know the stability of that correlation method. For this reason, it is essential to check the stability of the considered classical correlations and robust correlations so that we can use those correlations without any doubt in our mind. In this paper, several contamination cases have been introduced for checking the stability of the classical and robust correlations that are considered. The performances of robust correlations and classical correlations are compared and also performances of robust correlations among each other are compared through a simulation study and real data examples both for study clean data and contaminated data. Based on simulation study and real data applications, robust correlations have much better performance compared to classical correlations from clean to contaminated data. Among the robust correlations adjusted bivariate winsorized correlation has more stability than any other robust correlations. When some observations in real dataset are replaced by outliers, classical correlation i.e. Pearson correlation is changed drastically and robust
correlations remain almost same.