Efficient estimation of conditional covariance matrices for dimension reduction

Jean-Michel Loubes (1) , Clément Marteau (1) , Michael Solis (1) , Sébastien da Veiga (2, 3)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 IFPEN - IFP Energies nouvelles
3 GdR MASCOT-NUM - Méthodes d'Analyse Stochastique des Codes et Traitements Numériques

We consider the problem of estimating a conditional covariance matrix in an inverse regression setting. We show that this estimation can be achieved by estimating a quadratic functional extending the results of \citet{daveiga2008efficient}. We prove that this method provides a new efficient estimator whose asymptotic properties are studied.

Mots clés: dimension reduction; SIR method; efficient estimation

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Jean-Michel Loubes, Clément Marteau, Michael Solis, Sébastien da Veiga. Efficient estimation of conditional covariance matrices for dimension reduction. 2011. ⟨hal-00632576⟩