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
[email protected]
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Hovig Tanajian
Department of Biostatistics
New York State University at Buffalo
Buffalo, NY
[email protected]
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Alan D. Hutson
Department of Biostatistics
New York State University at Buffalo
Buffalo, NY
[email protected]
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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
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