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The Asymptotic Local Structure of the Cox Modified Likelihood-Ratio Statistic for Testing Non-Nested Hypotheses

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  • Szroeter, Jerzy

Abstract

It is shown that the Cox modified likelihood-ratio statistic for testing partially non-nested hypotheses H0 and H1 is asymptotically equivalent to a bilinear form in nondegenerate asymptotically normal random vectors for sequences of data-generating processes converging to the intersection of H0 and H1 but not necessarily belonging to either H0 or H1. One of the asymptotically normal vectors is the complete parametric encompassing vector of Mizon and Richard, while the other is a close relative. The results are valid regardless of whether or not the data-generating process is exponential and imply that the Cox statistic is not generally asymptotically locally normal. This corrects an assumption made in recent literature.

Suggested Citation

  • Szroeter, Jerzy, 1992. "The Asymptotic Local Structure of the Cox Modified Likelihood-Ratio Statistic for Testing Non-Nested Hypotheses," Econometric Theory, Cambridge University Press, vol. 8(4), pages 553-569, December.
    • Handle: RePEc:cup:etheor:v:8:y:1992:i:04:p:553-569_01
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    Cited by:

    1. Michelis, Leo, 1999. "The distributions of the J and Cox non-nested tests in regression models with weakly correlated regressors," Journal of Econometrics, Elsevier, vol. 93(2), pages 369-401, December.
    2. Szroeter, J., 1996. "Characterization of the exact finite-sample distribution of a routine test statistic for non-nested regressions," Statistics & Probability Letters, Elsevier, vol. 29(1), pages 9-14, August.

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