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December, 1993 Bootstrap Confidence Regions for Functional Relationships in Errors-in- Variables Models
James G. Booth, Peter Hall
Ann. Statist. 21(4): 1780-1791 (December, 1993). DOI: 10.1214/aos/1176349397

Abstract

We suggest bootstrap methods for constructing confidence bands (and intervals) for an unknown linear functional relationship in an errors-invariables model. It is assumed that the ratio of error variances is known to lie within an interval $\Lambda = \lbrack\lambda_1, \lambda_2\rbrack$. A confidence band is constructed for the range of possible linear relationships when $\lambda \in \Lambda$. Meaningful results are obtained even in the extreme case $\Lambda = \lbrack 0, \infty\rbrack$, which corresponds to no assumption being made about $\Lambda$. The bootstrap bands have several interesting features, which include the following: (i) the bands do not shrink to a line as $n \rightarrow \infty$, unless $\Lambda$ is a singleton (i.e., $\lambda_1 = \lambda_2)$; (ii) percentile-$t$ versions of the bands enjoy only first-order coverage accuracy, not the second-order accuracy normally found in simpler statistical problems.

Citation

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James G. Booth. Peter Hall. "Bootstrap Confidence Regions for Functional Relationships in Errors-in- Variables Models." Ann. Statist. 21 (4) 1780 - 1791, December, 1993. https://doi.org/10.1214/aos/1176349397

Information

Published: December, 1993
First available in Project Euclid: 12 April 2007

zbMATH: 0789.62035
MathSciNet: MR1245768
Digital Object Identifier: 10.1214/aos/1176349397

Subjects:
Primary: 62J05
Secondary: 62G15

Rights: Copyright © 1993 Institute of Mathematical Statistics

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Vol.21 • No. 4 • December, 1993
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