Rates of convergence in conditional covariance matrix with nonparametric entries estimation

2013/10/30 by Loubes, Jean-Michel, Marteau, Clement, Solís, Maikol
#FOS: Computer and information sciences #Methodology (stat.ME)

paper · doi:10.48550/arxiv.1310.8244

Abstract

Let X∈ ℝ^p and Y∈ ℝ be two random variables. We estimate the conditional covariance matrix Cov(E[\boldsymbolX\vert 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 (\boldsymbolX,Y). In a high-dimensional context, we improve the consistency the whole matrix estimator by providing a decreasing structure over the Cov(E[\boldsymbolX\vert Y]) entries. We illustrate a sliced inverse regression setting for time series matching the conditions of our estimator

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