title: Density-based empirical likelihood procedures for testing symmetry of data distributions and K-sample comparisons.
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 ofKgroups 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 comparesK-sample distributions. Recognizing that recent statistical software packages do not sufficiently addressK-sample nonparametric comparisons of data distributions, we propose a new Stata command, vxdbel, to execute exact density-based empirical likelihood-ratio tests usingKsamples. To calculatep-values of the proposed tests, we use the following methods: 1) a classical technique based on Monte Carlop-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-testp-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.
authors.affiliation: Department of Biostatistics, New York State University at Buffalo, Buffalo, NY.
authors.forename: Albert
authors.initials: A
authors.lastname: Vexler
authors.affiliation: Department of Biostatistics, New York State University at Buffalo, Buffalo, NY.
authors.forename: Hovig
authors.initials: H
authors.lastname: Tanajian
authors.affiliation: Department of Biostatistics, New York State University at Buffalo, Buffalo, NY.
authors.forename: Alan D
authors.initials: AD
authors.lastname: Hutson
keywords: K-sample comparisons; empirical likelihood; exact tests; likelihood ratio; nonparametric tests; p-value computation; st0338; symmetry; vxdbel