Different groups of robust estimators of a correlation coefficient are studied in asymptotics and by Monte Carlo. It is shown that the robust estimators based on the robust estimators of the variances of the linear transformations of the data are the best. Their best behavior is explained by the introduction of a new class of bidimensional distributions with heavy tails and by the consequent design of the corresponding robust minimax (in Huber sense) estimator of a correlation coefficient.
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