A consistent bayesian bootstrap for chi-squared goodness-of-fit test using a dirichlet prior

Abstract

In this paper, we employ the Dirichlet process in a hypothesis testing framework to propose a Bayesian nonparametric chi-squared goodness-of-fit test. Our suggested method corresponds to Lo’s Bayesian bootstrap procedure for chi-squared goodness of-fit test and rectifies some shortcomings of regular bootstrap which only counts number of observations falling in each bin in contingency tables. We consider the Dirichlet process as the prior for the distribution of the data and carry out the test based on the Kullback-Leibler distance between the updated Dirichlet process and the hypothesized distribution. Moreover, the results are generalized to chi-squared test of independence for a contingency table.