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Abstract:
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The main enemies of hypothesis testing procedures are (1) small sample sizes, (2) excessive nonresponse rate, and (3) high dimensionality. Their adverse effect can be reduced if additional information or guess about the distribution of alternatives can be incorporated into test statistics. If such information is too general (for example, only a parametrical family can be specified), this distribution is estimated from a principle of the most powerful testing. We investigate power properties of the proposed tests in the presence of the mentioned enemies and compare them with maximum likelihood estimators. Theoretical results, results of simulation studies and a missing data example are presented in the manuscript.
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