A Bayesian Chi-Squared Test for Hypothesis Testing

Yong Li (), Xiao-Bin Liu and Jun Yu
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Xiao-Bin Liu: Singapore Management University

No 03-2014, Working Papers from Singapore Management University, School of Economics

Abstract: A new Bayesian test statistic is proposed to test a point null hypothesis based on a quadratic loss. The proposed test statistic may be regarded as the Bayesian version of Lagrange multiplier test. Its asymptotic distribution is obtained based on a set of regular conditions and follows a chi-squared distribution when the null hypothesis is correct. The new statistic has several important advantages that make it appeal in practical applications. First, it is well-defined under improper prior distributions. Second, it avoids Jeffrey-Lindley’s paradox. Third, it is relatively easy to compute, even for models with latent variables. Finally, it is pivotal and its threshold value can be easily obtained from the asymptotic chi-squared distribution. The method is illustrated using some real examples in economics and finance.

Keywords: Bayes factor; Decision theory; EM algorithm; Lagrange multiplier; Markov chain Monte Carlo; Latent variable models (search for similar items in EconPapers)
JEL-codes: C11 C12 (search for similar items in EconPapers)
Pages: 29 pages
Date: 2014-06
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Published in SMU Economics and Statistics Working Paper Series

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Journal Article: A Bayesian chi-squared test for hypothesis testing (2015)
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