Supplementary Material: A Robust-Equitable Copula Dependence Measure for Feature Selection
نویسندگان
چکیده
For simplicity, we focus on the bivariate case (X and Y are each one-dimensional variables). The extension to proof in multivariate case is straight forward. We first work on the mutual information, then show the similar arguments on the copula distances. To prove the theorem, we use Le Cam [1973]’s method to find the lower bound on the minimax risk of the estimating mutual information MI . To do this, we will use a more convenient form of Le Cam’s method developed by Donoho and Liu [1991]. Define the module of continuity of a functional T over the class F with respect to Hellinger distance as in equation (1.1) of Donoho and Liu [1991]:
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