The Bayesian Score Statistic
AbstractWe 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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Bibliographic InfoPaper provided by Erasmus University Rotterdam, Econometric Institute in its series Econometric Institute Report with number EI ; ECONOMETRIC INSTITUTE REPORT 2000-16/A Revision_Date: 2009-07-29.
Date of creation: 19 Apr 2000
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Web page: http://www.few.eur.nl/few
Other versions of this item:
- Kleibergen, F.R. & Kleijn, R.H. & Paap, R., 2000. "The Bayesian Score Statistic," Econometric Institute Report EI 2000-16/A, Erasmus University Rotterdam, Econometric Institute.
- Frank Kleibergen & Richard Kleijn & Richard Paap, 2000. "The Bayesian Score Statistic," Tinbergen Institute Discussion Papers 00-035/4, Tinbergen Institute.
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