The main goal of this paper is to develop a numerical procedure for construction of covariance matrices such that for a given covariance structural model and a discrepancy function the corresponding minimizer of the discrepancy function has a specified value. Often construction of such matrices is a first step in Monte Carlo studies of statistical in- ferences of misspecified models. We analyze theoretical aspects of the problem, and suggest a numerical procedure based on semi-definite programming techniques. As an example, we discuss in details the factor analysis model.
School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0205, USA, 06/2008