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A lower bound using Hamilton-type circuits and its applications

Part of: Distribution theory Applications

Published online by Cambridge University Press:  14 July 2016

John T. Chen
John T. Chen*
Affiliation:
Bowling Green State University
*
∗Postal address: Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, OH 43403, USA. Email address: jchen@bgnet.bgsu.edu
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Abstract

This paper presents a degree-two probability lower bound for the union of an arbitrary set of events in an arbitrary probability space. The bound is designed in terms of the first-degree Bonferroni summation and pairwise joint probabilities of events, which are represented as weights of edges in a Hamilton-type circuit in a connected graph. The proposed lower bound strengthens the Dawson–Sankoff lower bound in the same way that Hunter and Worsley's degree-two upper bound improves the degree-two Bonferroni-type optimal upper bound. It can be applied to statistical inference in time series and outlier diagnoses as well as the study of dose response curves.

Keywords

Bonferroni-type boundDawson–Sankoff inequalitytraveling salesman problemHamilton-type circuitsoutlier detectionseasonal trendsdose-response curves

MSC classification

Primary: 62E15: Exact distribution theory
Secondary: 62P10: Applications to biology and medical sciences
Type
Research Papers
Information
Journal of Applied Probability , Volume 40 , Issue 4 , September 2003 , pp. 1121 - 1132
Copyright
Copyright © Applied Probability Trust 2003 

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