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An extended family of statistics is defined as a set of asymptotically-equivalent quadratic forms in a given vector where each component of a weighting matrix is any consistent estimator of an appropriate matrix. Given a type of information matrix (IM) equality, two statistics are said to be comparable if both statistics are constructed with the IM-type equality imposed or both constructed with the...
For a model where a type of information matrix equality holds, the literature provides explicit forms for a score-type and a Hausman-type statistic based on particular nonsingular generalized inverses. This paper provides similar explicit forms for a more general model where a type of information matrix equality does not necessarily (but may) hold.
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