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March, 1994 Confidence Regions in Linear Functional Relationships
Heping Zhang
Ann. Statist. 22(1): 49-66 (March, 1994). DOI: 10.1214/aos/1176325357

Abstract

A unified approach to deriving confidence regions in linear functional relationship models is presented, based on the conditional likelihood ratio method of Knowles, Siegmund and Zhang. In the case of a single latent predictor, the confidence region for the slope produced by this approach is the familiar one of Fieller and Creasy. However, here it is shown how to derive a confidence region for the slope, when it is known that the slope is positive, that improves on merely intersecting the region for an unrestricted slope with $(0,\infty)$. A geometric interpretation is given for Fieller-Creasy confidence region for the ratio of population means (Fieller-Creasy problem). Regions are also derived for simultaneous estimation of the slope and intercept in the model with a single latent predictor, and for the slopes in a model with two latent predictors.

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Heping Zhang. "Confidence Regions in Linear Functional Relationships." Ann. Statist. 22 (1) 49 - 66, March, 1994. https://doi.org/10.1214/aos/1176325357

Information

Published: March, 1994
First available in Project Euclid: 11 April 2007

zbMATH: 0816.62030
MathSciNet: MR1272075
Digital Object Identifier: 10.1214/aos/1176325357

Subjects:
Primary: 62F25
Secondary: 62E15, 62J02

Rights: Copyright © 1994 Institute of Mathematical Statistics

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Vol.22 • No. 1 • March, 1994
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