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Efficient estimation of conditional covariance matrices for dimension reduction

Sébastien da Veiga 1 Jean-Michel Loubes 2 Maikol Solís 3
1 IFPEN - IFP Energies nouvelles
2 IMT - Institut de Mathématiques de Toulouse UMR5219
3 Universidad Nacional de Costa Rica
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
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Submitted on : Wednesday, July 19, 2017 - 12:07:30 PM
Last modification on : Friday, January 7, 2022 - 3:46:18 AM

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Sébastien da Veiga, Jean-Michel Loubes, Maikol Solís. Efficient estimation of conditional covariance matrices for dimension reduction. Communications in Statistics - Theory and Methods, Taylor & Francis, 2017, 46 (9), pp.4403 - 4424. ⟨10.1080/03610926.2015.1083109⟩. ⟨hal-01564965⟩

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