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Journal of the American Statistical Association Volume 81, 1986 - Issue 393
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Theory and Method

Asymptotic Theory of Overparameterized Structural Models

Alexander Shapiro Department of Mathematics and Applied Mathematics, University of South Africa, P.O. Box 392, Pretoria, 0001, South Africa
Pages 142-149 | Received 01 May 1983, Published online: 12 Mar 2012
 
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Abstract

A theory of overparameterized structural models is presented. In such a model some “redundant” parameters are involved; the parameter vector is not identified, and the information matrix is not nonsingular. The minimum discrepancy function (MDF) test statistic is shown to have an asymptotic chi-squared distribution almost everywhere for a wide class of discrepancy functions. Asymptotic distribution properties of the MDF estimators are investigated. The factor analysis model is discussed as an example.

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