Asymptotics of goodness-of-fit tests based on minimum p-value statistics |
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Authors: | Veronika Gontscharuk Helmut Finner |
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Institution: | Institute for Biometrics and Epidemiology, German Diabetes Center, Leibniz Institute for Diabetes Research at Heinrich-Heine-University Düsseldorf, Düsseldorf, Germany |
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Abstract: | This paper provides some new results on the asymptotics of goodness-of-fit (GOF) tests based on minimum p-value statistics. In connection with detectability of sparse signals in high-dimensional data, various tests were proposed and investigated during the last decade, especially with respect to asymptotic properties. Minimum p-value GOF statistics were already investigated as minimum level attained statistics by Berk and Jones with respect to Bahadur efficiency. The distribution of minimum p-value GOF statistics is closely related to the distribution of higher criticism statistics, the distribution of the supremum of a normalized Brownian bridge, and the supremum of an Ornstein–Uhlenbeck process. |
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Keywords: | Equal local levels goodness-of-fit higher criticism Kolmogorov–Smirnov test minimum level attained order statistics |
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