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Alternative Asymptotically Optimal Tests and Their Application to Dynamic Specification

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  • Richard J Smith

Abstract

A method is presented for generating test statistics which share the same first order asymptotic optimality properties of the classical statistics. Generalizing Neyman's (1959) work, the linearised classical statistic tests restrictions in implicit function form using a parameter estimator which is consistent and asymptotically normally distributed under the alternative hypothesis. By judicious choice of estimator and form of restrictions at which to evaluate the statistic, a class of asymptotically optimal statistics is obtained among which are numbered some familiar classical statistics. An application is presented for testing common factor restrictions in a single equation dynamic regression model with moving average disturbances.

Suggested Citation

  • Richard J Smith, 1987. "Alternative Asymptotically Optimal Tests and Their Application to Dynamic Specification," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 54(4), pages 665-680.
    • Handle: RePEc:oup:restud:v:54:y:1987:i:4:p:665-680.
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    File URL: http://hdl.handle.net/10.2307/2297488
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    Cited by:

    1. Dogan, Osman & Taspinar, Suleyman & Bera, Anil K., 2017. "Simple Tests for Social Interaction Models with Network Structures," MPRA Paper 82828, University Library of Munich, Germany.
    2. Brown, Kenneth & Cribari-Neto, Francisco, 1992. "On Hypothesis Testing: A Selective Look at the Lagrange Multiplier, Likelihood Ratio and Wald Tests," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 12(2), November.
    3. Jean-Marie Dufour & Alain Trognon & Purevdorj Tuvaandorj, 2017. "Invariant tests based on M -estimators, estimating functions, and the generalized method of moments," Econometric Reviews, Taylor & Francis Journals, vol. 36(1-3), pages 182-204, March.
    4. Smith, Richard J., 2011. "Gel Criteria For Moment Condition Models," Econometric Theory, Cambridge University Press, vol. 27(6), pages 1192-1235, December.
    5. MacKinnon, James G, 1992. "Model Specification Tests and Artificial Regressions," Journal of Economic Literature, American Economic Association, vol. 30(1), pages 102-146, March.
    6. Xuexin Wang, 2020. "A new class of tests for overidentifying restrictions in moment condition models," Econometric Reviews, Taylor & Francis Journals, vol. 39(5), pages 495-509, May.
    7. Joann Jasiak & Purevdorj Tuvaandorj, 2023. "Penalized Likelihood Inference with Survey Data," Papers 2304.07855, arXiv.org.
    8. Richard Smith, 2004. "GEL Criteria for Moment Condition Models," CeMMAP working papers 19/04, Institute for Fiscal Studies.
    9. Joann Jasiak & Peter MacKenzie & Purevdorj Tuvaandorj, 2023. "Digital Divide: Empirical Study of CIUS 2020," Papers 2301.07855, arXiv.org, revised Oct 2024.

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