parametric rate of convergence of $O\left(1/N\right)$. The weight $w_{0}$ is the solution to the offline convex optimization problem *$$\begin{array}{rl}
\min_{w} & ||w||_{2}\\
subject\,to & \sum_{l\in\mathcal{L}}w(l)=1,\\
 & \gamma_{w}(i)=\sum_{l\in\mathcal{L}}w(l)\psi_{i}(l)=0,\,i\in J.
\end{array}\label{eq:optimize}$$*

To apply Theorem \[thm:opt\_weight\] to an ensemble of estimators, all $\phi_{i}(N)$ functions that converge to zero slower than $1/\sqrt{N}$ and the corresponding $\psi_{i}(l)$ functions must be known for the base estimator. Otherwise, Theorem \[thm:opt\_weight\] can only be guaranteed to improve the bias up to the slowest unknown bias rate. This theorem was applied in [@moon2016isit] to the problem of divergence functional estimation where the plug-in estimator has slowly converging bias but the resulting ensemble estimator achieves the parametric rate for sufficiently smooth densities.

We apply Theorem \[thm:opt\_weight\] to the ensemble estimator $\g{w,1}$ as conditions $\mathcal{C}.1$ and $\mathcal{C}.2$ are satisfied with $\phi_{i}(N)=N^{-i/(2d_{X})}$ and $\psi_{i}(l)=l^{i}$ for $i\in\{1,\dots r\}$ as seen in (\[eq:bias\_mixed1\]) and (\[eq:weight\_bias\]). If $s\geq d_{X}$, then the MSE of the optimally weighted estimator $\g{w_{0},1}$ is $O(1/N)$. A similar approach can be used for the case where $\X$ contains a mixture of continuous and discrete components and $\Y$ is discrete (or vice versa). To the best of our knowledge, these are the first nonparametric estimators to achieve the MSE parametric rate in 