Robust Estimation of a Correlation Coefficient for Ε-contaminated Bivariate Normal Distributions

Robust estimators of a correlation coefficient based on: (i) direct robust counterparts of the sample correlation coefficient, (ii) nonparametric measures of correlation, (iii) robust regression, (iv) robust estimation of the variances of principal variables, (v) stable parameter estimation, and (vi) the preliminary rejection of outliers from the data with the subsequent application of the sample correlation coefficient to the rest of the observations, are considered. Their performance in ε-contaminated normal models is examined both on small and large samples, and the best of the proposed robust estimators are revealed.