On similarity and independence properties of composite edf goodness-of-fit tests |
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Authors: | CP Quesenberry |
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Institution: | North Carolina State University Raleigh , North Carolina, 2765O |
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Abstract: | Many test statistics for classical simple goodness-of-fit hypothesis testing problems are distancemeasures between the distribution function of the null hypothesis distributipn and the empirical distribution function sometimes called EDF tests. If a composite parametric null hypothesis is considered in place of the simple null hypothesis, then a test statistic can be obtained from each EDF test by replacing the known distribution function of the simple problem by the Rao-Blackwell estimating distribution function. In this note we use known results to show that these Rao-Blackwell-EDF test statistics have distributions that do not depend upon parameter values, and hence that these tests are independent of a complete sufficient statistic for the parameters. |
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Keywords: | Rao Blackwell estimators similar tests invariance transitivity sufficiency completeness |
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