A Bayesian robust chi-squared test for testing simple hypotheses

In this paper, we introduce a new Bayesian chi-squared test based on an adjusted quadratic loss function for testing a simple null hypothesis. We show that the asymptotic null distribution of our suggested test is a central chi-squared distribution under some assumptions required for the Bayesian large sample theory. We refer to our test as the Bayesian robust chi-squared test, since it is robust to parametric misspecification in the alternative model. That is, the limiting null distribution of our test is a central chi-squared distribution irrespective of parametric misspecification in the alternative model. In addition to being robust to parametric misspecification, our test also shares properties of the test suggested by Li et al. (2015) based on a quadratic loss function. We provide four examples to illustrate the implementation of our suggested Bayesian test statistic.