the asymptotic bias and variance results for divergence estimators [@moon2016isit; @moon2016arxiv] to kernel density plug-in MI estimators without boundary correction [@karunamuni2005boundary] by incorporating machinery to handle the dependence between the product of marginal density estimators (Section \[sec:MI\_est\]), (2) we extend the theory to handle discrete random variables in the mixed cases (cases 2 and 3) by reformulating the densities as a mixture of the conditional density of the continuous variables given the discrete variables (Section \[sec:mixed\]), and (3) we leverage this theory for the mixed cases in conjunction with the generalized theory of ensemble estimators [@moon2016arxiv; @moon2016isit] to derive, to the best of our knowledge, the first non-parametric estimator that achieves a parametric rate of MSE convergence of $O\left(1/N\right)$ for the mixed cases (Section \[sec:mixed\_ensemble\]), where $N$ is the number of samples available from each distribution. We also derive a central limit theorem for the ensemble estimators (Section \[subsec:clt\]). We verify the theory through experiments (Section \[sec:experiments\]).

Continuous Random Variables {#sec:MI_est}
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In this section, we obtain MSE convergence rates of plug-in MI estimators when $\X$ and $\Y$ are continuous (case 1 in Section \[sec:intro\]). This will enable us to derive the MSE convergence rates of plug-in MI estimators when 