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Conflict Among the Criteria Revisited; The W, LR and LM Tests

G. B. A. Evans
N. E. Savin

Abstract

In the classical linear regression model the conflict between the W, LR, and LM tests is due to the tests not having the correct significance level. This paper shows that the probability of conflict can be substantial when the three tests are based on the asymptotic chi-square critical value. For this model some computable correction factors for the chi-square critical values are examined, including those derived from a second-order Edgeworth approximation to the exact distributions. It is shown that the probability of conflict between the Edgeworth size-corrected tests is of no practical importance over a wide range of conditions.