A two-sample empirical likelihood ratio test based on samples entropy |
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Authors: | Gregory Gurevich Albert Vexler |
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Institution: | 1.The Department of Industrial Engineering and Management,SCE—Shamoon College of Engineering,Beer Sheva,Israel;2.Department of Biostatistics,New York State University at Buffalo,Buffalo,USA |
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Abstract: | Powerful entropy-based tests for normality, uniformity and exponentiality have been well addressed in the statistical literature.
The density-based empirical likelihood approach improves the performance of these tests for goodness-of-fit, forming them
into approximate likelihood ratios. This method is extended to develop two-sample empirical likelihood approximations to optimal
parametric likelihood ratios, resulting in an efficient test based on samples entropy. The proposed and examined distribution-free
two-sample test is shown to be very competitive with well-known nonparametric tests. For example, the new test has high and
stable power detecting a nonconstant shift in the two-sample problem, when Wilcoxon’s test may break down completely. This
is partly due to the inherent structure developed within Neyman-Pearson type lemmas. The outputs of an extensive Monte Carlo
analysis and real data example support our theoretical results. The Monte Carlo simulation study indicates that the proposed
test compares favorably with the standard procedures, for a wide range of null and alternative distributions. |
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