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Testing Nonnested Linear Hypotheses I : Reduction By Invariance Considerations

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  • Bouman, J.

Abstract

This paper is concerned with the problem of testing nonnested linear hypotheses. The problem is expressed in terms of the relevant linear (vector) subspaces. The "degree of nonnestedness" of the hypotheses is examined. After a suitable linear transformation, the vector of observations is reduced by invariance considerations to a 2—dimensional statistic. It is shown that the power function of invariant tests depends on the regressor matrices through certain characteristic numbers which measure "the degree of nonnestedness" of the linear hypotheses.

Suggested Citation

  • Bouman, J., 1984. "Testing Nonnested Linear Hypotheses I : Reduction By Invariance Considerations," Econometric Institute Archives 272284, Erasmus University Rotterdam.
    • Handle: RePEc:ags:eureia:272284
    DOI: 10.22004/ag.econ.272284
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    References listed on IDEAS

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    1. Pesaran, M H & Deaton, Angus S, 1978. "Testing Non-Nested Nonlinear Regression Models," Econometrica, Econometric Society, vol. 46(3), pages 677-694, May.
    2. Davidson, Russell & MacKinnon, James G, 1981. "Several Tests for Model Specification in the Presence of Alternative Hypotheses," Econometrica, Econometric Society, vol. 49(3), pages 781-793, May.
    3. M. H. Pesaran, 1974. "On the General Problem of Model Selection," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 41(2), pages 153-171.
    4. Fisher, Gordon R. & McAleer, Michael, 1981. "Alternative procedures and associated tests of significance for non-nested hypotheses," Journal of Econometrics, Elsevier, vol. 16(1), pages 103-119, May.
    5. Dastoor, Naorayex K., 1983. "Some aspects of testing non-nested hypotheses," Journal of Econometrics, Elsevier, vol. 21(2), pages 213-228, February.
    6. Godfrey, Leslie G, 1983. "Testing Non-Nested Models after Estimation by Instrumental Variables or Least Squares," Econometrica, Econometric Society, vol. 51(2), pages 355-365, March.
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    Cited by:

    1. Bouman, J., 1986. "Testing Nonnested Linear Hypotheses Ii: Some Invariant Exact Tests," Econometric Institute Archives 272352, Erasmus University Rotterdam.
    2. Bouman, J., 1985. "Testing Nonnested Linear Hypotheses: A Bayesian Approach Based On Incompletely Specified Prior Distributions," Econometric Institute Archives 272325, Erasmus University Rotterdam.

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