A new Bayesian test statistic is proposed to test a point null hypothesis based on 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.
Bayes factor; Decision theory; EM algorithm; Lagrange multiplier; Markov chain Monte Carlo; Latent variable models.
LI, Yong; Liu, Xiao-Bin; and YU, Jun.
A Bayesian Chi-Squared Test for Hypothesis Testing. (2014). Research Collection School Of Economics.
Available at: http://ink.library.smu.edu.sg/soe_research/1588
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