A Bayesian nonparametric chi-squared goodness-of-fit test

The Bayesian nonparametric inference and Dirichlet process are popular tools in statistical methodologies. In this paper, we employ the Dirichlet process in hypothesis testing to propose a Bayesian nonparametric chi-squared goodness-of-fit test. In our Bayesian nonparametric approach, we consider the Dirichlet process as the prior for the distribution of data and carry out the test based on the Kullback-Leibler distance between the updated Dirichlet process and the hypothesized distribution F0. We prove that this distance asymptotically converges to the same chi-squared distribution as the chi-squared test does. Similarly, a Bayesian nonparametric chi-squared test of independence for a contingency table is provided. Also, by computing the Kullback-Leibler distance between the Dirichlet process and the hypothesized distribution, a method to obtain an appropriate concentration parameter for the Dirichlet process is suggested.