Econometrics Commons^™

A Bayesian Chi-Squared Test For Hypothesis Testing, Yong Li, Xiaobin Liu, Jun Yu

Research Collection School Of Economics

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 …