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Biometrika 1982 69(2):297-302; doi:10.1093/biomet/69.2.297
© 1982 by Biometrika Trust
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An improved Bonferroni inequality and applications

K. J. WORSLEY

Department of Mathematics, McGill University Montreal, Quebec, Canada

We present an improved Bonferroni inequality which gives an upper bound for the probability of the union of an arbitrary sequence of events. The bound is constructed in terms of the joint probability of pairs of events, which are represented by edges on a graph. Examples of applications to periodicity, location shift detection, Kolmogorov-Smirnov tests and outlier detection are given.

Key Words: Bonferroni inequality • Periodicity • Location shift detection • Kolmogorov-Smirnov test • Outlier


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