Rates of convergence in conditional covariance matrix with nonparametric entries estimation

Jean-Michel Loubes, Clément Marteau and Maikol Solís

Communications in Statistics - Theory and Methods, 2020, vol. 49, issue 18, 4536-4558

Abstract: Given X∈Rp and Y∈R two random variables, assume the model Y=ψ(X)+ε where ψ(·) is an unknown function and ε is a random error. We estimate the conditional covariance matrix Cov(E[X|Y]) applying a plug-in kernel-based algorithm to its entries. Next, we investigate the estimators rate of convergence under smoothness hypotheses on the density function of (X,Y). In a high-dimensional context, we improve the consistency the whole matrix estimator by providing a decreasing structure over the Cov(E[X|Y]) entries. We illustrate a sliced inverse regression setting with a simulation study.

Date: 2020
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DOI: 10.1080/03610926.2019.1602652

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