Frequentist-Bayes Nonparametric Goodness-of-Fit Testing

• Activity Number: 238
• Type: Contributed
• Date/Time: Monday, August 4, 2014 : 2:00 PM to 3:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Taeryon Choi*+ and Jeffrey D. Hart and Seongbaek Yi and Hyungjoon Kim
• Companies: Korea University and Texas A&M and Pukyoung National University and Korea University
• Keywords: Bandwidth selection ; Bayes factor ; Empricial null distribution ; Goodness-of-fit tests ; Kernel density estimates

Abstract

In this paper, we propose a nonparametric frequentist-Bayes procedure for testing the goodness of fit of a parametric model. The test statistic is a Bayes factor in which the two marginal likelihoods being compared correspond to a kernel estimate and the parametric model. The marginal likelihood for the kernel estimate is obtained by proposing a prior for the estimate's bandwidth, and then integrating the product of this prior and a leave-one out kernel likelihood. While Bayesian principles are used to construct the statistic, the test is done in frequentist fashion by comparing the Bayes factor with its null percentiles. Monte Carlo is used to compare the power of the new test with that of the Shapiro-Wilk test in the important case of testing for normality. Comparisons with a nonparametric likelihood ratio test are also provided. In addition, the method is illustrated with real data examples, and its generalization is discussed.