Efficient estimation of conditional covariance matrices for dimension reduction
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.