Correction: A class of Rényi information estimators for multidimensional densities

Abstract

and Hq = ^(1 ? f^m fq(x)dx), q ^ 1, of an unknown probability measure with density / on Rm with respect to the Lebesgue measure though kth nearest neighbor distances in a sample X\,..., Xjy i.i.d. with the density /. The results in [1] about the asymptotic unbiasedness and consistency of the estimator proposed for Iq = E{fq~l(X)} = fRm fq(x)dx are correct for q > 1 but, for q 0: fmm \x\rf(x)dx rc(/)(see[2]). A correct version of the convergence results of lN,k,q to for 0 < g < 1 and / having unbounded support can be obtained by using results on the sub additivity of Euclidean functionals (see [3]) and can be formulated as follows [2]: