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Let $X\in \mathbb{R}^p$ and $Y\in \mathbb{R}$ be two random variables. Weestimate the conditional covariance matrix$\mathrm{Cov}\left(\mathrm{E}\left[\boldsymbol{X}\vert Y\right]\right)$applying a plug-in kernel-based algorithm to its entries. Next, we investigatethe estimators rate of convergence under smoothness hypotheses on the densityfunction of $(\boldsymbol{X},Y)$. In a high-dimensional context, we improve theconsistency the whole matrix estimator by providing a decreasing structure overthe $\mathrm{Cov}\left(\mathrm{E}\left[\boldsymbol{X}\vert Y\right]\right)$entries. We illustrate a sliced inverse regression setting for time seriesmatching the conditions of our estimator

Rates of convergence in conditional covariance matrix with nonparametric entries estimation