A Bayesian Chi-Squared Test for Hypothesis Testing

• Main Authors: LI, Yong, LIU, Xiao-Bin, YU, Jun
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2014
• Subjects: Bayes factor; Decision theory; EM algorithm; Lagrange multiplier; Markov chain Monte Carlo; Latent variable models.; Econometrics
• Online Access: https://ink.library.smu.edu.sg/soe_research/1588; https://ink.library.smu.edu.sg/context/soe_research/article/2587/viewcontent/03_2014.pdf
• Institution: Singapore Management University

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.