On a class of nonparametric tests for the treatment vs control problem |
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Authors: | KL Mehra KS Madhava Rao |
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Institution: | Department of Statistics and Applied Probability , University of Alberta , Edmonton, Alberta, T6G 2G1, Canada |
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Abstract: | The classical problem of testing treatment versus control is revisited by considering a class of test statistics based on a kernel that depends on a constant ‘a’. The proposed class includes the celebrated Wilcoxon-Mann-Whitnet statistics as a special case when ‘a’=1. It is shown that, with optimal choice of ‘a’ depending on the underlying distribution, the optimal member performs better (in terms of Pitman efficiency) than the Wilcoxon-Mann-Whitney and the Median tests for a wide range of underlying distributions. An extended Hodges-Lehmann type point estimator of the shift prameter corresponding to the proposed ‘optimal’ test statistic is also derived. |
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Keywords: | Hodges-Lehmann estimator nonparametric optimal test Pitman efficiency |
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