The Annals of Statistics

Events which are Almost Independent

R. L. Dykstra, John E. Hewett, and W. A. Thompson, Jr.

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Abstract

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.

Article information

Source
Ann. Statist., Volume 1, Number 4 (1973), 674-681.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176342462

Digital Object Identifier
doi:10.1214/aos/1176342462

Mathematical Reviews number (MathSciNet)
MR397815

Zentralblatt MATH identifier
0264.62004

JSTOR
links.jstor.org

Citation

Dykstra, R. L.; Hewett, John E.; Thompson, W. A. Events which are Almost Independent. Ann. Statist. 1 (1973), no. 4, 674--681. doi:10.1214/aos/1176342462. https://projecteuclid.org/euclid.aos/1176342462


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