On the exact Berk-Jones statistics and their p-value calculation
By Amit Moscovich, Boaz Nadler, Clifford H. Spiegelman. 2013
55 citations recorded by the source corpus.
Continuous goodness-of-fit testing is a classical problem in statistics. Despite having low power for detecting deviations at the tail of a distribution, the most popular test is based on the Kolmogorov-Smirnov statistic. While similar variance-weighted statistics, such as Anderson-Darling and the Higher Criticism statistic give more weight to tail deviations, as shown in various works, they still mishandle the extreme tails. As a viable alternative, in this paper we study some of the statistical properties of the exact $M_n$ statistics of Berk and Jones. We derive the asymptotic null distributions of $M_n, M_n^+, M_n^-$, and further prove their consistency as well as asymptotic optimality for a wide range of rare-weak mixture models. Additionally, we present a new computationally efficient method to calculate $p$-values for any supremum-based one-sided statistic, including the one-sided $M_n^+,M_n^-$ and $R_n^+,R_n^-$ statistics of Berk and Jones and the Higher Criticism statistic. We illustrate our theoretical analysis with several finite-sample simulations.
Subfields: Artificial Intelligence, Management Science and Operations Research, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/4aa2e3709ab05f7bb79c1b994904b814d63f78e9
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In Artificial Intelligence
In Management Science and Operations Research
In Statistics and Probability
Citations in the corpus
- Comparing distributions by multiple testing across quantiles or CDF values (2017, methodology): “Other papers have explored implications of the same probability integral transform, such as Moscovich, Nadler, and Spiegelman (2016) and Moscovich and Nadler (2017) in the computer science literature, but only for GOF testing or uniform confidence bands, never quantile multiple testing.”