A Robust Similarity Estimator

We construct and analyze an estimator of association between random variables based on their similarity in both direction and magnitude. Under special conditions, the proposed measure becomes a robust and consistent estimator of the linear correlation, for which an exact sampling distribution is available. This distribution is intrinsically insensitive to heavy tails and outliers, thereby facilitating robust inference for correlations. The measure can be naturally extended to higher dimensions, where it admits an interpretation as an indicator of joint similarity among multiple random variables. We investigate the empirical performance of the proposed measure with financial return data at both high and low frequencies. Specifically, we apply the new estimator to construct confidence intervals for correlations based on intraday returns and to develop a new specification for multivariate GARCH models.

💡 Research Summary

The paper introduces a novel estimator of association between two random variables that captures both directional agreement and magnitude similarity. Starting from Thorndike’s “resemblance” measure
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