Minimax variance estimation of a correlation coefficient for [var epsilon]-contaminated bivariate normal distributions

A minimax variance (in the Huber sense) estimator of a correlation coefficient for [var epsilon]-contaminated bivariate normal distributions is given by the trimmed correlation coefficient. Consistency and asymptotic normality of this estimator are established, and the explicit expression for its asymptotic variance is obtained. The limiting cases of this estimator are the sample correlation coefficient with [var epsilon]=0 and the median correlation coefficient as [var epsilon]-->1. In [var epsilon]-contaminated normal models, the proposed trimmed correlation coefficient is superior in efficiency than the sample correlation coefficient.