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September, 1977 On the Uniformity of Sequential Procedures
Raymond J. Carroll
Ann. Statist. 5(5): 1039-1046 (September, 1977). DOI: 10.1214/aos/1176343958

Abstract

An extension of a central limit theorem for a mean of a random number of observations is given. A natural application occurs in the area of fixed-width confidence intervals. We provide an example which shows that the standard procedure does not preserve the intended coverage probability uniformly over nontrivial sets of distribution functions. The major weak convergence result is used to provide conditions for and a simple proof of such uniformity. The results are also shown to hold for $M$-estimates of location.

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Raymond J. Carroll. "On the Uniformity of Sequential Procedures." Ann. Statist. 5 (5) 1039 - 1046, September, 1977. https://doi.org/10.1214/aos/1176343958

Information

Published: September, 1977
First available in Project Euclid: 12 April 2007

zbMATH: 0368.62069
MathSciNet: MR451573
Digital Object Identifier: 10.1214/aos/1176343958

Subjects:
Primary: 62L99
Secondary: 62F07

Keywords: Sequential confidence intervals , two-dimensional processes , weak convergence

Rights: Copyright © 1977 Institute of Mathematical Statistics

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Vol.5 • No. 5 • September, 1977
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