The Annals of Statistics

Very Weak Expansions for Sequentially Designed Experiments: Linear Models

Michael Woodroofe

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Abstract

In sequentially designed experiments with linear models, each design variable may depend on previous responses. The use of such sequential designs does not affect the likelihood function or the functional form of the maximum likelihood estimator, but it may affect sampling distributions. In this paper, asymptotic expansions for sampling distributions are obtained. The expansions are very weak ones in which a confidence curve (a function of the unknown parameters) is replaced by a confidence functional defined on a class of prior distributions. The proofs use a version of Stein's identity.

Article information

Source
Ann. Statist., Volume 17, Number 3 (1989), 1087-1102.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176347257

Digital Object Identifier
doi:10.1214/aos/1176347257

Mathematical Reviews number (MathSciNet)
MR1015139

Zentralblatt MATH identifier
0683.62039

JSTOR
links.jstor.org

Subjects
Primary: 62E20: Asymptotic distribution theory
Secondary: 62F12: Asymptotic properties of estimators 62L05: Sequential design

Keywords
Martingale convergence theorem maximum likelihood estimators posterior distributions Stein's identity

Citation

Woodroofe, Michael. Very Weak Expansions for Sequentially Designed Experiments: Linear Models. Ann. Statist. 17 (1989), no. 3, 1087--1102. doi:10.1214/aos/1176347257. https://projecteuclid.org/euclid.aos/1176347257


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