A Bayesian chi-squared test for hypothesis testing
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 the 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 appealing in practical applications. First, it is well-defined under improper prior distributions. Second, it avoids Jeffrey-Lindley's paradox. Third, it always takes a non-negative value and is relatively easy to compute, even for models with latent variables. Fourth, its numerical standard error is relatively easy to obtain. Finally, it is asymptotically pivotal and its threshold values can be obtained from the chi-squared distribution. The method is illustrated using some real examples in economics and finance.
Bayes factor, Decision theory, EM algorithm, Lagrange multiplier, Markov chain Monte Carlo, Latent variable models
Journal of Econometrics
LI, Yong; LIU XIAOBIN; and Jun YU.
A Bayesian chi-squared test for hypothesis testing. (2015). Journal of Econometrics. 189, (1), 54-69. Research Collection School Of Economics.
Available at: http://ink.library.smu.edu.sg/soe_research/1862
Copyright Owner and License
Authors with CC-BY-NC-ND
Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.