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The Bayesian Score Statistic

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Author Info
Frank Kleibergen () (University of Amsterdam)
Richard Kleijn () (Erasmus University Rotterdam)
Richard Paap () (Erasmus University Rotterdam)

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Abstract

We propose a novel Bayesian test under a (noninformative) Jeffreys' prior specification. We check whether the fixed scalar value of the so- called Bayesian Score Statistic (BSS) under the null hypothesis is a plausible realization from its known and standardized distribution under the alternative. Unlike highest posterior density regions the BSS is invariant to reparameterizations. The BSS equals the posterior expectation of the classical score statistic and it provides an exact test procedure, whereas classical tests often rely on asymptotic results. Since the statistic is evaluated under the null hypothesis it provides the Bayesian counterpart of diagnostic checking. This result extends the similarity of classical sampling densities of maximum likelihood estimators and Bayesian posterior distributions based on Jeffreys' priors, towards score statistics. We illustrate the BSS as a diagnostic to test for misspecification in linear and cointegration models.

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Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 00-035/4.

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Date of creation: 27 Apr 2000
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Handle: RePEc:dgr:uvatin:20000035

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  1. Kleibergen, F. & Zivot, E., 1998. "Bayesian and Classical Approaches to Instrumental Variable Regression," Papers 9835/a, Erasmus University of Rotterdam - Econometric Institute.
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  2. Kleibergen, F.R. & Zivot, E., 1998. "Bayesian and classical approaches to instrumental variable regression," Econometric Institute Report EI 9835 Revision_Date: 20, Erasmus University Rotterdam, Econometric Institute. [Downloadable!]
  3. repec:cup:etheor:v:10:y:1994:i:3-4:p:514-51 is not listed on IDEAS
  4. Engle, Robert F & Granger, Clive W J, 1987. "Co-integration and Error Correction: Representation, Estimation, and Testing," Econometrica, Econometric Society, vol. 55(2), pages 251-76, March. [Downloadable!] (restricted)
  5. Kleibergen, Frank & Paap, Richard, 2002. "Priors, posteriors and bayes factors for a Bayesian analysis of cointegration," Journal of Econometrics, Elsevier, vol. 111(2), pages 223-249, December. [Downloadable!] (restricted)
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  6. Kleibergen, F.R. & Van Dijk, H.K., 1993. "On the Shape of the Likelyhood/Posterior in Cointegration Models," Papers 9315-a, Erasmus University of Rotterdam - Econometric Institute.
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  7. Frank R. Kleibergen, 2000. "Exact Test Statistics and Distributions of Maximum Likelihood Estimators that result from Orthogonal Parameters," Tinbergen Institute Discussion Papers 00-039/4, Tinbergen Institute. [Downloadable!]
  8. Johansen, Soren, 1991. "Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models," Econometrica, Econometric Society, vol. 59(6), pages 1551-80, November. [Downloadable!] (restricted)
  9. Geweke, J, 1993. "Bayesian Treatment of the Independent Student- t Linear Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(S), pages S19-40, Suppl. De. [Downloadable!] (restricted)
  10. Chao, J. C. & Phillips, P. C. B., 1998. "Posterior distributions in limited information analysis of the simultaneous equations model using the Jeffreys prior," Journal of Econometrics, Elsevier, vol. 87(1), pages 49-86, August. [Downloadable!] (restricted)
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