Smoothed average variance estimation for dimension reduction with functional data

Abstract

We propose an estimation method, named functional average vari- ance estimation (FAVE), for estimating the EDR space in functional semiparametric regression model, based on kernel estimates of dens- ity and regression. Consistency results are then established for the estimator of the interest operator, and for the directions of EDR space. A simulation study that shows that the proposed approach performs better than traditional ones is presented