Open Access
March, 1976 On Confidence Sequences
Tze Leung Lai
Ann. Statist. 4(2): 265-280 (March, 1976). DOI: 10.1214/aos/1176343406


This paper is concerned with confidence sequences, i.e., sequences of confidence regions which contain the true parameter for every sample size simultaneously at a prescribed level of confidence. By making use of generalized likelihood ratio martingales, confidence sequences are constructed for the unknown parameters of the binomial, Poisson, uniform, gamma and other distributions. It is proved that for the exponential family of distributions, the method of using generalized likelihood ratio martingales leads to a sequence of intervals which have the desirable property of eventually shrinking to the population parameter. The problem of nuisance parameters is considered, and in this connection, boundary crossing probabilities are obtained for the sequence of Student's $t$-statistics, and a limit theorem relating to the boundary crossing probabilities for the Wiener process is proved.


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Tze Leung Lai. "On Confidence Sequences." Ann. Statist. 4 (2) 265 - 280, March, 1976.


Published: March, 1976
First available in Project Euclid: 12 April 2007

zbMATH: 0346.62035
MathSciNet: MR395103
Digital Object Identifier: 10.1214/aos/1176343406

Primary: 62F25
Secondary: 62L10

Keywords: boundary crossing probabilities , Confidence sequences , Invariance , likelihood ratio martingales , nuisance parameters , Student's $t$-statistics

Rights: Copyright © 1976 Institute of Mathematical Statistics

Vol.4 • No. 2 • March, 1976
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