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Rates of convergence in conditional covariance matrix with nonparametric entries estimation

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  • Jean-Michel Loubes
  • Clément Marteau
  • Maikol Solís

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.

Suggested Citation

  • Jean-Michel Loubes & Clément Marteau & Maikol Solís, 2020. "Rates of convergence in conditional covariance matrix with nonparametric entries estimation," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 49(18), pages 4536-4558, September.
    • Handle: RePEc:taf:lstaxx:v:49:y:2020:i:18:p:4536-4558
    DOI: 10.1080/03610926.2019.1602652
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    Cited by:

    1. Nathan Kallus & Xiaojie Mao, 2023. "Stochastic Optimization Forests," Management Science, INFORMS, vol. 69(4), pages 1975-1994, April.

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