Bayesian empirical likelihood methods for quantile comparisons

Albert Vexler, Jihnhee Yu, Nicole Lazar

Research output: Contribution to journalArticlepeer-review

Abstract

Bayes factors, practical tools of applied statistics, have been dealt with extensively in the literature in the context of hypothesis testing. The Bayes factor based on parametric likelihoods can be considered both as a pure Bayesian approach as well as a standard technique to compute p-values for hypothesis testing. We employ empirical likelihood methodology to modify Bayes factor type procedures for the nonparametric setting. The paper establishes asymptotic approximations to the proposed procedures. These approximations are shown to be similar to those of the classical parametric Bayes factor approach. The proposed approach is applied towards developing testing methods involving quantiles, which are commonly used to characterize distributions. We present and evaluate one and two sample distribution free Bayes factor type methods for testing quantiles based on indicators and smooth kernel functions. An extensive Monte Carlo study and real data examples show that the developed procedures have excellent operating characteristics for one-sample and two-sample data analysis.

Original languageEnglish (US)
Pages (from-to)518-538
Number of pages21
JournalJournal of the Korean Statistical Society
Volume46
Issue number4
DOIs
StatePublished - Dec 2017

All Science Journal Classification (ASJC) codes

  • Statistics and Probability

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