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Likelihood ratio specification tests
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DOI：10.2307/2171756.png)
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Abstract
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Misspecification tests for parametric models, f(y, theta), that examine data for failure of moment conditions implied by the maintained parametric distribution are interpreted as score tests of H-0: lambda = 0 in the context of a parametric family of distributions r(y; theta, lambda). This family contains the maintained distribution as a special case (lambda = 0) and has the property that only in that special case do the chosen moment conditions hold. A likelihood ratio test of H-0: lambda = 0 therefore constitutes an alternative test of the validity of the moment conditions. This test admits a Bartlett correction, unlike conventional moment tests for which adjustments based on second order asymptotic theory may behave badly. The dependence of the Bartlett correction and of the O(n(-1/2)) local power of the test on the way in which r(y; theta, lambda) is constructed is studied. In many cases the correction can be made to vanish leading to a specification test whose distribution is chi-square to order O-p((n-2)).
Keywords:
Bartlett correction
Edgeworth expansion
local power
moment tests
parametric model
score test
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