Asymptotically minimax bias estimation of the correlation coefficient for bivariate independent component distributions

Abstract

For bivariate independent component distributions, the asymptotic bias of the correlation coefficient estimators based on principal component variances is derived. This result allows to design an asymptotically minimax bias (in the Huber sense) estimator of the correlation coefficient, namely, the trimmed correlation coefficient, for contaminated bivariate normal distributions. The limit cases of this estimator are the sample, median and MAD correlation coefficients, the last two simultaneously being the most B- and V-robust estimators. In contaminated normal models, the proposed estimators dominate both in bias and in efficiency over the sample correlation coefficient on small and large samples.