Statistical inference in non-nested econometric models. (English) Zbl 0658.62134
The purpose of this paper is to discuss some procedures that are available for testing non-nested (or separate) hypotheses in the statistics and econometrics literature. Since many of these techniques may also be exploited in other disciplines, it is hoped that an elaboration of the principal theoretical findings may make them more readily accessible to researchers in other disciplines. Several simple examples are used to illustrate the concepts of nested and non-nested hypotheses and, within the latter category, “global” and “partial” non-nested hypotheses.
Two alternative methods of testing non-nested hypotheses are discussed and contrasted: the first of these is D. R. Cox’s modification of the likelihood-ratio statistic [Proc. of the 4th Berk. Symp. on Math. Stat. and Probab., Vol. 1, Univ. of Calif. Press, Berkeley, 105-123 (1961; Zbl 0201.521) and J. R. Stat. Soc., Ser. B 24, 406-424 (1962; Zbl 0131.358)], and the second is A. C. Atkinson’s comprehensive model approach [ibid., B 32, 323-353 (1970; Zbl 0225.62020)]. A major emphasis is placed on the role of the Cox principle of hypothesis testing, which enables a broad range of hypotheses to be tested within the same framework.
The problem associated with the application of the comprehensive model approach to composite non-nested hypotheses is also highlighted; S. N. Roy’s union-intersection principle [Ann. Math. Stat. 24, 220-238 (1953; Zbl 0051.367)] is presented as a viable method of dealing with this problem. Simulation results concerning the finite-sample properties of various tests are discussed, together with an analysis of some attempts to correct the poor size of the Cox and related tests.
Two alternative methods of testing non-nested hypotheses are discussed and contrasted: the first of these is D. R. Cox’s modification of the likelihood-ratio statistic [Proc. of the 4th Berk. Symp. on Math. Stat. and Probab., Vol. 1, Univ. of Calif. Press, Berkeley, 105-123 (1961; Zbl 0201.521) and J. R. Stat. Soc., Ser. B 24, 406-424 (1962; Zbl 0131.358)], and the second is A. C. Atkinson’s comprehensive model approach [ibid., B 32, 323-353 (1970; Zbl 0225.62020)]. A major emphasis is placed on the role of the Cox principle of hypothesis testing, which enables a broad range of hypotheses to be tested within the same framework.
The problem associated with the application of the comprehensive model approach to composite non-nested hypotheses is also highlighted; S. N. Roy’s union-intersection principle [Ann. Math. Stat. 24, 220-238 (1953; Zbl 0051.367)] is presented as a viable method of dealing with this problem. Simulation results concerning the finite-sample properties of various tests are discussed, together with an analysis of some attempts to correct the poor size of the Cox and related tests.
MSC:
| 62P20 | Applications of statistics to economics |
| 62J05 | Linear regression; mixed models |
| 62H15 | Hypothesis testing in multivariate analysis |
Keywords:
testing non-nested hypotheses; Cox’s modification of the likelihood-ratio statistic; Atkinson’s comprehensive model approach; composite non-nested hypotheses; Roy’s union-intersection principle; Simulation results; finite-sample propertiesReferences:
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