The Annals of Statistics

On Confidence Sequences

Tze Leung Lai

Full-text: Open access

Abstract

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.

Article information

Source
Ann. Statist., Volume 4, Number 2 (1976), 265-280.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176343406

Digital Object Identifier
doi:10.1214/aos/1176343406

Mathematical Reviews number (MathSciNet)
MR395103

Zentralblatt MATH identifier
0346.62035

JSTOR
links.jstor.org

Subjects
Primary: 62F25: Tolerance and confidence regions
Secondary: 62L10: Sequential analysis

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

Citation

Lai, Tze Leung. On Confidence Sequences. Ann. Statist. 4 (1976), no. 2, 265--280. doi:10.1214/aos/1176343406. https://projecteuclid.org/euclid.aos/1176343406


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