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Global and Partial Non-Nested Hypotheses and Asymptotic Local Power

Published online by Cambridge University Press:  11 February 2009

M. Hashem Pesaran
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Abstract

This paper addresses two related issues in the literature of non-nested hypotheses testing. Firstly, by means of a measure of “closeness” of probability density functions, it shows how any two hypotheses can be placed into the nested and the non-nested categories with the latter category being subdivided further into “globally” and “partially” non-nested hypotheses. Secondly, by emphasizing the distinction between a “local null” and a “local alternative,” the paper shows that only in the case of partially non-nested hypotheses is it possible to specify local alternatives. In this case the paper derives the asymptotic distribution of the Cox test statistic under local alternatives and shows that it is distributed as a normal variate with a mean which is directly related to the measure of “closeness” of the alternative to the null hypothesis.

Type
Research Article
Information
Econometric Theory , Volume 3 , Issue 1 , February 1987 , pp. 69 - 97
Copyright
Copyright © Cambridge University Press 1987

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References

REFERENCES

1. Abramowitz, M. and Stegun, I. A. (Eds.), Handbook of Mathematical Functions. National Bureau of Standards, Washington, D.C., 1964.Google Scholar
2. Akaike, H. Information theory and an extension of the likelihood principles, in Petrov, B. N. and Csaki, F. (Eds.), Proceedings of the Second International Symposium of Information Theory. Budapest, Akadémiai Kiado, 1973.Google Scholar
3. Bahadur, R. R. Stochastic comparison of tests. Annals of Mathematical Statistics 31 (1960): 276–295.10.1214/aoms/1177705894CrossRefGoogle Scholar
4. Bahadur, R. R. Rates of convergence of estimates and test statistic. Annals of Mathematical Statistics 38 (1967): 303–324.10.1214/aoms/1177698949CrossRefGoogle Scholar
5. Burbea, J. and Rao, C. R.. Entropy differential metric, distance and divergence measures in probability spaces: A unified approach. Journal of Multivariate Analysis 12 (1982): 575–596.10.1016/0047-259X(82)90065-3CrossRefGoogle Scholar
6. Cox, D. R. Tests of separate families of hypotheses. Proceedings of the 4th Berkeley Symposium 1 (1961): 105–123.Google Scholar
7. Cox, D. R. Further results on tests of separate families of hypotheses. Journal of Royal Statistical Society B, 24 (1962): 406–424.Google Scholar
8. Dastoor, N. K. Some aspects of testing non-nested hypotheses. Journal of Econometrics 21 (1983): 213–228.CrossRefGoogle Scholar
9. Davidson, R. and Mackinnon, J.. Several tests for model specification in the presence of alternative hypotheses. Econometrica 49 (1981): 781–793.10.2307/1911522CrossRefGoogle Scholar
10. Davidson, R. and Mackinnon, J.. Some non-nested hypothesis tests and the relations among them. Review of Economic Studies 49 (1982): 551–565.10.2307/2297286CrossRefGoogle Scholar
11. Deaton, A. S. Model selection procedures, or, Does the consumption function exist?, in Chow, C. G. and Corsi, P. (Eds.), Evaluating the Reliability of Macroeconomic Models. New York: Wiley (1982): 43–65.Google Scholar
12. Fisher, G. R. and McAleer, M.. Alternative procedures and associated tests of significance for non-nested hypotheses. Journal of Econometrics 16 (1981): 103–119.10.1016/0304-4076(81)90078-6CrossRefGoogle Scholar
13. Gourieroux, C., Monfort, A., and Trognon, A.. Testing nested or non-nested hypotheses. Journal of Econometrics 21 (1983): 83–115.10.1016/0304-4076(83)90121-5CrossRefGoogle Scholar
14. Jackson, O.A.Y. Some results on tests of separate families of hypotheses. Biometrika 55 (1968): 355–363.10.1093/biomet/55.2.355CrossRefGoogle Scholar
15. Kent, J. T. Robust properties of likelihood ratio tests. Biometrika 69 (1982): 19–27.Google Scholar
16. Kullback, S. Information Theory and Statistics. New York: Wiley, 1959.Google Scholar
17. Kullback, S. and Leibler, R. A.. On information and sufficiency. Annals of Mathematical Statistics 22 (1951): 79–86.CrossRefGoogle Scholar
18. Pesaran, M. H. On the general problem of model selection. Review of Economic Studies 41 (1974): 153–171.10.2307/2296710CrossRefGoogle Scholar
19. Pesaran, M. H. Comparison of local power of alternative tests of non-nested regression models. Econometrica 50 (1982): 1287–1305.10.2307/1911874CrossRefGoogle Scholar
20. Pesaran, M. H. Asymptotic power comparisons of tests of separate parametric families by Bahadur's approach. Biometrika 71 (1984): 245–252.CrossRefGoogle Scholar
21. Pesaran, M. H. and Deaton, A. S.. Testing non-nested nonlinear regression models. Econo metrica 46 (1978): 677–694.10.2307/1914240CrossRefGoogle Scholar
22. Prentice, R. L. A log-gamma model and its maximum likelihood estimation. Biometrika 61 (1974): 539–544.10.1093/biomet/61.3.539CrossRefGoogle Scholar
23. Sawyer, K. R. Testing separate families of hypotheses: An information criterion. Journal of Statistical Society B, 45 (1983): 89–99.Google Scholar
24. Shen, S. M. A method for discriminating between models describing compositional data. Biometrika 69 (1982): 587–595.CrossRefGoogle Scholar
25. White, H. Maximum likelihood estimation of misspecified models. Econometrica 50 (1982a): 1–25.10.2307/1912526CrossRefGoogle Scholar
26. White, H. Regularity conditions for Cox's test of non-nested hypotheses. Journal of Econometrics 19 (1982b): 301–318.CrossRefGoogle Scholar