A General Method of Testing for Random Parameter Variation in Statistical Models
Testing the adequacy of an estimated statistical model is a perennial problem for data analysts. If some specific alternative construction of the model is entertained—for example, if allowance should be made for autocorrelation—then it is fairly straightforward to write down specific test statistics tailored for that situation. On the other hand, in many circumstances what is required is some indication of the overall suitability of the model rather looking in some specific direction. In cases where the model can be formulated in such a way that maximum likelihood (or pseudo maximum likelihood) methods may be used, an elegant technique was introduced by White (1982) which exploits the well known information-matrix equality that holds for properly specified models. If the specified model is not consistent with the data, this equality will not hold; and this fact may be used as the basis for a general specification test.
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