Goodness-of-Fit measures

Abstract

In the preceding chapters statistical, structural linear models have been discussed in a minimum distance setting. The linear relations between the components of the random vector X are described by the model parameters, which are in the Principal Relations (PR) case represented by a (k×p) matrix B and in the Principal Factors (PF) case by means of a (k×q) matrix A. Application of the method of moments technique yields consistent estimators of B and A and using the delta method, their limiting distributions can be obtained. The asymptotic variances of the parameter estimators give some information on the spread of the values of the estimates about the population value. That is, the variance indicates how well the population parameter is estimated by this specific sample. But it does not say anything about the credibility of the linear specification itself.