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Asymptotics of goodness-of-fit tests based on minimum p-value statistics

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  • Veronika Gontscharuk
  • Helmut Finner

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.

Suggested Citation

  • Veronika Gontscharuk & Helmut Finner, 2017. "Asymptotics of goodness-of-fit tests based on minimum p-value statistics," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(5), pages 2332-2342, March.
    • Handle: RePEc:taf:lstaxx:v:46:y:2017:i:5:p:2332-2342
    DOI: 10.1080/03610926.2015.1041985
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