E-optimal block designs under heteroscedastic model

Abstract

This paper mainly studies the E-optimality of block designs under a general heteroscedastic setting. The C-matrix of a block design under a heteroscedastic setting is obtained by using generalized least squares. Some bounds for the smallest positive eigenvalue of C-matrix are obtained in some general classes of connected designs. Use of these bounds is then made to obtain certain E-optimal block designs in various classes of connected block designs.