Density-based empirical likelihood procedures for testing symmetry of data distributions and K-sample comparisons

Area of Science:

• Statistics
• Nonparametric Statistics
• Computational Statistics

Background:

• Parametric likelihood-ratio techniques are established statistical tools.
• Existing statistical software inadequately addresses K-sample nonparametric distribution comparisons.
• Need for efficient, distribution-free methods to analyze and compare multiple data distributions.

Purpose of the Study:

• To propose and examine novel, distribution-free test statistics approximating parametric likelihood ratios.
• To develop a Stata package for density-based empirical likelihood analysis of K-sample distributions.
• To introduce a new Stata command, vxdbel, for exact K-sample nonparametric comparisons.

Main Methods:

• Utilized density-based empirical likelihood methodology.
• Developed a Stata package and the 'vxdbel' command for K-sample distribution comparison.
• Employed three p-value calculation methods: Monte Carlo, interpolation, and a novel hybrid Bayesian-type approach.

Main Results:

• Proposed novel distribution-free test statistics efficiently approximate parametric likelihood ratios.
• The new Stata command 'vxdbel' enables exact density-based empirical likelihood-ratio tests for K samples.
• The hybrid Bayesian-type method for p-value computation is highly efficient for exact tests.

Conclusions:

• The proposed distribution-free statistics and Stata command provide efficient tools for K-sample nonparametric comparisons.
• The novel hybrid p-value computation method offers significant efficiency gains.
• This work addresses a gap in statistical software for complex distribution comparisons.