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

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

Domains: Mathematics [math]

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