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

Veronika Gontscharuk and Helmut Finner

Communications in Statistics - Theory and Methods, 2017, vol. 46, issue 5, 2332-2342

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.

Date: 2017
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DOI: 10.1080/03610926.2015.1041985

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