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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.
Alexander Shapiro (Sat,) studied this question.