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July, 1973 Events which are Almost Independent
R. L. Dykstra, John E. Hewett, W. A. Thompson Jr.
Ann. Statist. 1(4): 674-681 (July, 1973). DOI: 10.1214/aos/1176342462


Often, the probability of the simultaneous occurrence of dependent events can be well approximated by assuming them to be independent. Here, we discuss bounds on the error in using this procedure and conditions when under (or over) estimates occur. An inequality involving expectations of conditionally independent random variables is proven. Applications treat extreme values of exchangeable random variables and error probabilities for simultaneous inference. Bivariate dependence concepts treated by Lehmann are generalized to the multivariate case in such a way that relations valid for the bivariate case continue to hold.


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R. L. Dykstra. John E. Hewett. W. A. Thompson Jr.. "Events which are Almost Independent." Ann. Statist. 1 (4) 674 - 681, July, 1973.


Published: July, 1973
First available in Project Euclid: 12 April 2007

zbMATH: 0264.62004
MathSciNet: MR397815
Digital Object Identifier: 10.1214/aos/1176342462

Rights: Copyright © 1973 Institute of Mathematical Statistics


Vol.1 • No. 4 • July, 1973
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