Construction of Covariance Matrices with a Specified Discrepancy Function Minimizer, with Application to Factor Analysis

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 inferences 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. Key words. Model misspecification, covariance structure analysis, maximum likelihood, generalized least squares, discrepancy function, factor analysis, semi-definite programming. AMS subject classifications. 62H25, 90C26

• Type: Journal
• Year: 2010
• Where: SIAMMAX
• Authors: So Yeon Chun, A. Shapiro
• Keywords: Discrepancy Function, Factor Analysis, Numerical Procedure, SIAMMAX 2010