Bayesian Empirical Likelihood Methods for Quantile Comparisons.

Area of Science:

• Statistics
• Bayesian statistics
• Nonparametric statistics

Background:

• Bayes factors are established tools for hypothesis testing in parametric settings.
• Parametric Bayes factors can be viewed as both a pure Bayesian method and a p-value computation technique.
• Existing methods often lack flexibility for nonparametric data structures.

Purpose of the Study:

• To adapt Bayes factor methodology for nonparametric hypothesis testing.
• To develop novel testing procedures for quantiles using empirical likelihood.
• To establish asymptotic properties of the proposed nonparametric Bayes factor.

Main Methods:

• Utilizing empirical likelihood methodology to modify Bayes factor procedures.
• Developing one and two sample distribution-free Bayes factor type methods.
• Employing indicators and smooth kernel functions for quantile testing.
• Establishing asymptotic approximations for the modified Bayes factor.

Main Results:

• The proposed nonparametric Bayes factor procedures have asymptotic approximations similar to classical parametric approaches.
• The methods are effective for testing quantiles, crucial for distribution characterization.
• Both one-sample and two-sample distribution-free tests were developed and evaluated.
• Extensive simulations and real data examples confirm the procedures' efficacy.

Conclusions:

• The empirical likelihood-based Bayes factor provides a robust nonparametric alternative for hypothesis testing.
• The developed methods demonstrate excellent operating characteristics for quantile-based analysis.
• This approach extends the utility of Bayes factors to a broader range of statistical problems.