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The Large Sample Correspondence between Classical Hypothesis Tests and Bayesian Posterior Odds Tests

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  • Andrews, Donald W K

Abstract

This paper establishes a correspondence in large samples between classical hypothesis tests and Bayesian posterior odds tests for models without trends. More specifically, tests of point null hypotheses and one- or two-sided alternatives are considered (where nuisance parameters may be present under both hypotheses). It is shown that, for certain priors, the Bayesian posterior odds test is equivalent in large samples to classical Wald, Lagrange multiplier, and likelihood ratio tests for some significance level and vice versa. The priors considered under the alternative hypothesis are taken to shrink to the null hypothesis at rate n[superscript -1/2] as the sample size n increases. Copyright 1994 by The Econometric Society.

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  • Andrews, Donald W K, 1994. "The Large Sample Correspondence between Classical Hypothesis Tests and Bayesian Posterior Odds Tests," Econometrica, Econometric Society, vol. 62(5), pages 1207-1232, September.
    • Handle: RePEc:ecm:emetrp:v:62:y:1994:i:5:p:1207-32
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    Cited by:

    1. Hoshino, Takahiro, 2008. "Bayesian significance testing and multiple comparisons from MCMC outputs," Computational Statistics & Data Analysis, Elsevier, vol. 52(7), pages 3543-3559, March.
    2. Ghysels, Eric & Guay, Alain, 2003. "Structural change tests for simulated method of moments," Journal of Econometrics, Elsevier, vol. 115(1), pages 91-123, July.
    3. Chernozhukov, Victor & Hong, Han, 2003. "An MCMC approach to classical estimation," Journal of Econometrics, Elsevier, vol. 115(2), pages 293-346, August.
    4. Penelope Smith, 2006. "Bayesian Inference for a Threshold Autoregression with a Unit Root," Melbourne Institute Working Paper Series wp2006n20, Melbourne Institute of Applied Economic and Social Research, The University of Melbourne.
    5. Götz, Thomas B. & Hecq, Alain & Smeekes, Stephan, 2016. "Testing for Granger causality in large mixed-frequency VARs," Journal of Econometrics, Elsevier, vol. 193(2), pages 418-432.
    6. Pablo Guerrón-Quintana & Atsushi Inoue & Lutz Kilian, 2009. "Frequentist inference in weakly identified DSGE models," Working Papers 09-13, Federal Reserve Bank of Philadelphia.
    7. Ghysels, Eric & Guay, Alain, 2004. "Testing For Structural Change In The Presence Of Auxiliary Models," Econometric Theory, Cambridge University Press, vol. 20(6), pages 1168-1202, December.
    8. Kim, Jae-Young, 2014. "An alternative quasi likelihood approach, Bayesian analysis and data-based inference for model specification," Journal of Econometrics, Elsevier, vol. 178(P1), pages 132-145.
    9. Berg, Nathan, 2004. "No-decision classification: an alternative to testing for statistical significance," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 33(5), pages 631-650, November.
    10. Lavergne, Pascal, 2014. "Model equivalence tests in a parametric framework," Journal of Econometrics, Elsevier, vol. 178(P3), pages 414-425.

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