Efficient estimation of conditional covariance matrices for dimension reduction

Sébastien da Veiga; Jean-Michel Loubes; Maikol Solís

Efficient estimation of conditional covariance matrices for dimension reduction

Sébastien da Veiga ¹ Jean-Michel Loubes ² Maikol Solís ³

2 IMT - Institut de Mathématiques de Toulouse UMR5219

Abstract : Let X ∈ Rp andY ∈ R. In this paper,we propose an estimator of the conditional covariancematrix, Cov(E[X|Y]), in an inverse regression setting. Based on the estimation of a quadratic functional, this methodology provides an efficient estimator from a semi parametric point of view.We consider a functional Taylor expansion of Cov(E[X|Y]) under some mild conditions and the effect of using an estimate of the unknown joint distribution. The asymptotic properties of this estimator are also provided.

Keywords : Conditional covariance matrix Inverse sliced regression Efficient estimation Tarylor expansion Semiparametric estimation

Document type :

Journal articles

Domain :

Mathematics [math]

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https://hal-ifp.archives-ouvertes.fr/hal-01564965
Contributor : Françoise Bertrand <>
Submitted on : Wednesday, July 19, 2017 - 12:07:30 PM
Last modification on : Thursday, October 17, 2019 - 8:53:24 AM

Efficient estimation of conditional covariance matrices for dimension reduction

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Efficient estimation of conditional covariance matrices for dimension reduction

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