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Construction of exact simultaneous confidence bands for a simple linear regression model

Liu, Wei, Lin, Shan and Piegorsch, Walter W. (2008) Construction of exact simultaneous confidence bands for a simple linear regression model International Statistical Review, 76, (1), pp. 39-57. (doi:10.1111/j.1751-5823.2007.00027.x).

Record type: Article

Abstract

A simultaneous confidence band provides a variety of inferences on the unknown components of a regression model. There are several recent papers using confidence bands for various inferential purposes; see for example, Sun et al. (1999), Spurrier (1999), Al-Saidy et al. (2003), Liu et al. (2004), Bhargava & Spurrier (2004), Piegorsch et al. (2005) and Liu et al. (2007). Construction of simultaneous confidence bands for a simple linear regression model has a rich history, going back to the work of Working & Hotelling (1929). The purpose of this article is to consolidate the disparate modern literature on simultaneous confidence bands in linear regression, and to provide expressions for the construction of exact 1 ?? level simultaneous confidence bands for a simple linear regression model of either one-sided or two-sided form. We center attention on the three most recognized shapes: hyperbolic, two-segment, and three-segment (which is also referred to as a trapezoidal shape and includes a constant-width band as a special case). Some of these expressions have already appeared in the statistics literature, and some are newly derived in this article. The derivations typically involve a standard bivariate t random vector and its polar coordinate transformation.

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More information

Published date: 7 March 2008
Keywords: simple linear regression, simultaneous inferences, bivariate normal, bivariate t, polar coordinators

Identifiers

Local EPrints ID: 55204
URI: http://eprints.soton.ac.uk/id/eprint/55204
ISSN: 0306-7734
PURE UUID: 6e2fca7e-608a-44d6-b493-3b4266509b54
ORCID for Wei Liu: ORCID iD orcid.org/0000-0002-4719-0345

Catalogue record

Date deposited: 05 Aug 2008
Last modified: 17 Jul 2017 14:33

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Contributors

Author: Wei Liu ORCID iD
Author: Shan Lin
Author: Walter W. Piegorsch

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