Home  >>  Archives  >>  Volume 14 Number 2  >>  st0338

The Stata Journal
Volume 14 Number 2: pp. 304-328

Subscribe to the Stata Journal

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

Albert Vexler
Department of Biostatistics
New York State University at Buffalo
Buffalo, NY
Hovig Tanajian
Department of Biostatistics
New York State University at Buffalo
Buffalo, NY
Alan D. Hutson
Department of Biostatistics
New York State University at Buffalo
Buffalo, NY
Abstract.  In practice, parametric likelihood-ratio techniques are powerful statistical tools. In this article, we propose and examine novel and simple distribution-free test statistics that efficiently approximate parametric likelihood ratios to analyze and compare distributions of K groups of observations. Using the density-based empirical likelihood methodology, we develop a Stata package that applies to a test for symmetry of data distributions and compares K-sample distributions. Recognizing that recent statistical software packages do not sufficiently address K-sample nonparametric comparisons of data distributions, we propose a new Stata command, vxdbel, to execute exact density-based empirical likelihood-ratio tests using K samples. To calculate p-values of the proposed tests, we use the following methods: 1) a classical technique based on Monte Carlo p-value evaluations; 2) an interpolation technique based on tabulated critical values; and 3) a new hybrid technique that combines methods 1 and 2. The third, cutting-edge method is shown to be very efficient in the context of exact-test p-value computations. This Bayesian-type method considers tabulated critical values as prior information and Monte Carlo generations of test statistic values as data used to depict the likelihood function. In this case, a nonparametric Bayesian method is proposed to compute critical values of exact tests.

View all articles by these authors: Albert Vexler, Hovig Tanajian, Alan D. Hutson

View all articles with these keywords: vxdbel, empirical likelihood, likelihood ratio, nonparametric tests, exact tests, K-sample comparisons, symmetry, p-value computation

Download citation: BibTeX  RIS

Download citation and abstract: BibTeX  RIS

Contact StataCorp

Contact service@stata-journal.com if you have questions about the Stata Journal.

© Copyright 2001–2014 StataCorp LP.   Terms of use.   Privacy policy.