Correction: A class of Rényi information estimators for multidimensional densities

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Nonparametric Divergence Estimation with Applications to Machine Learning on Distributions (2011, background): “The original presentations of these works contained some errors; Leonenko and Pronzato (2010) provide corrections for some of these theorems.”
A class of Rényi information estimators for multidimensional densities (2008, background): “The results in [1] about the asymptotic unbiasedness and consistency of the estimator proposed for Iq = E{f q−1(X)} = ∫Rm f (x) dx are correct for q > 1 but, for q < 1, convergence in distribution should be complemented by additional arguments to obtain the required convergence of moments.”
On the Estimation of alpha-Divergences (2011, unknown): “The original presentations of these works contained some errors; Leonenko and Pronzato (2010) provide corrections for some of these theorems.”
On the Estimation of α-Divergences (2011, background): “We also demonstrate in that section how our divergence es- 1The original presentations of these works contained some errors; Leonenko and Pronzato (2010) provide corrections for some of these theorems. timators can be used for Rényi- and Tsallis-mutual information (mi) estimation.”
On the Kozachenko-Leonenko entropy estimator (2016, background): “In [10], a consistency result is proved (for HN defined by (2)), in any dimension, under rather weak conditions on f and this is generalized to other notions of entropies by Leonenko, Pronzato and Savani in [11].”