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Националния семинар по стохастика

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Tests of stochastic dominance with repeated measurements data

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Ангел Ангелов (ФМИ – СУ).

Абстракт: We explore a testing problem which involves four hypotheses, i.e., based on observations of two random variables X and Y, we wish to discriminate between four possibilities: identical survival functions, stochastic dominance of X over Y, stochastic dominance of Y over X, or crossing survival functions. Four-decision testing procedures for repeated measurements data are proposed. The tests are based on a permutation approach and do not rely on distributional assumptions. One-sided versions of the Cramér–von Mises, Anderson–Darling, and Kolmogorov–Smirnov statistics are considered. The consistency of the tests is shown. A simulation study indicates good power properties and control of false-detection errors. The proposed tests are applied to data from a psychophysical experiment.