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A Posterior-Based Wald-Type Statistic for Hypothesis Testing

Yong Li (), Xiaobin Liu (), Tao Zeng () and Jun Yu ()
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Yong Li: Renmin University of China
Xiaobin Liu: Zhejiang University
Tao Zeng: Zhejiang University

No 8-2018, Economics and Statistics Working Papers from Singapore Management University, School of Economics

Abstract: A new Wald-type statistic is proposed for hypothesis testing based on Bayesian posterior distributions. The new statistic can be explained as a posterior version of Wald test and have several nice properties. First, it is well-defi ned under improper prior distributions. Second, it avoids Jeffreys-Lindley's paradox. Third, under the null hypothesis and repeated sampling, it follows a x2 distribution asymptotically, offering an asymptotically pivotal test. Fourth, it only requires inverting the posterior covariance for the parameters of interest. Fifth and perhaps most importantly, when a random sample from the posterior distribution (such as an MCMC output) is available, the proposed statistic can be easily obtained as a by-product of posterior simulation. In addition, the numerical standard error of the estimated proposed statistic can be computed based on the random sample. The finite sample performance of the statistic is examined in Monte Carlo studies. The method is applied to two latent variable models used in microeconometrics and financial econometrics.

Keywords: Decision theory; Hypothesis testing; Latent variable models; Posterior simulation; Wald test. (search for similar items in EconPapers)
JEL-codes: C11 C12 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-ecm and nep-ore
Date: 2018-05-11
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