Improving estimated sufficient summary plots in dimension reduction using minimization criteria based on initial estimates

Abstract

In this paper we show that estimated sufficient summary plots can be greatly improved when the dimension reduction estimates are adjusted according to minimization of an objective function. The dimension reduction methods primarily considered are ordinary least squares, sliced inverse regression, sliced average variance Estimates and principal Hessian directions. Some consideration to minimum average variance estimation is also given. Simulations support the usefulness of the approach and three data sets are considered with an emphasis on two- and three-dimensional estimated sufficient summary plots.