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June, 1985 Estimation in the General Linear Model when the Accuracy is Specified Before Data Collection
Mark Finster
Ann. Statist. 13(2): 663-675 (June, 1985). DOI: 10.1214/aos/1176349546

Abstract

An estimator $\hat{\beta}$ of $\beta$ is accurate with accuracy $A$ and confidence $\gamma, 0 < \gamma < 1,$ if $P(\hat{\beta} - \beta \in A) \geq \gamma$ for all $\beta.$ Given a sequence $Y_1, Y_2, \cdots$ of independent vector-valued homoscedastic normally-distributed random variables generated via the general linear model $Y_i = X_i\beta + \varepsilon,$ the $k$-dimensional parameter $\beta$ is accurately estimated using a sequential version of the maximum probability estimator developed by L. Weiss and J. Wolfowitz. The procedure given also generalizes C. Stein's fixed-width confidence sets to several dimensions.

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Mark Finster. "Estimation in the General Linear Model when the Accuracy is Specified Before Data Collection." Ann. Statist. 13 (2) 663 - 675, June, 1985. https://doi.org/10.1214/aos/1176349546

Information

Published: June, 1985
First available in Project Euclid: 12 April 2007

zbMATH: 0589.62067
MathSciNet: MR790564
Digital Object Identifier: 10.1214/aos/1176349546

Subjects:
Primary: 62L12
Secondary: 60G40, 62E20

Rights: Copyright © 1985 Institute of Mathematical Statistics

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Vol.13 • No. 2 • June, 1985
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