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

So Yeon Chun (gth586a***at***mail.gatech.edu)
Alexander Shapiro (ashapiro***at***isye.gatech.edu)

Abstract: 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.

Keywords: Model misspecification, covariance structure analysis, maximum likelihood, generalized least squares, discrepancy function, factor analysis, semi-definite programming.

Category 1: Applications -- OR and Management Sciences

Citation: School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0205, USA, 06/2008

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Entry Submitted: 06/13/2008
Entry Accepted: 06/13/2008
Entry Last Modified: 05/28/2009

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