BAYESIAN SEMIPARAMETRIC INFERENCE BASED ON RANKS IN ONE-SAMPLE LOCATION MODELS
Xiaojiang Zhan, Thomas P. Hettmansperger · 2005
summary When prior information exists, it would be desirable to incorporate it in the data analysis, even when we are using robust rank-based methods. In this paper we discuss the implementation of nonparametric rank-based procedures in the Bayesian context. We summarize the information in a sample of data via the (possibly asymptotic) distribution of some rank-based quantity, and use that distribution as a pseudo-likelihood. Meanwhile, we suppose a prior distribution for the parameter(s) of interest in the unknown function. By Bayes’ theorem, we can obtain the complete posterior distribution (or the posterior distribution up to a normalizing constant) of the parameter(s) given the rank-based quantity. Statistical inference then proceeds based on this posterior distribution. The onesample location model is considered using several rank-based quantities defined from common scores statistics such as the sign statistic, the Wilcoxon signed rank statistic and the normal scores statistic.