Sankhya: The Indian Journal of Statistics

2002, Volume 64, Series A, Pt. 1, pp. 109--138

THE BEHAVIOUR OF LINEAR MODEL SELECTION TESTS UNDER GLOBALLY NON-NESTED HYPOTHESES

By

MITCHELL R. WATNIK and WESLEY O. JOHNSON, University of California, Davis

SUMMARY. We consider the asymptotic behaviour of tests for non-nested linear model selection under the alternative hypothesis. We consider three testing procedures: the J-test (cf. Davidson and MacKinnon, 1981); the JA-test (cf. Fisher and McAleer, 1981); and the modified Cox test (cf. Godfrey and Pesaran, 1983). All are shown to have positive means under the true alternative. Thus, for discriminating between models, they should be treated as one-sided tests. We derive asymptotic distributions for slightly modified versions of these statistics under the alternative in order to obtain relative efficiencies. The modified versions are selected since they have greater power than the original test statistics. Both algebraic and theoretical relationships among the tests are indicated.

AMS (1991) subject classification. Primary 62J05, 62F05; secondary 62J15, 62F03.

Key words and phrases. Asymptotic relative efficiency; j-test; JA-test; Multiple correlation; Power; Regression; Separate hypotheses.

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