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), 39-57. (doi:10.1111/j.1751-5823.2007.00027.x).

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Description/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 −α 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.

Item Type: Article
ISSNs: 0306-7734 (print)
Related URLs:
Keywords: simple linear regression, simultaneous inferences, bivariate normal, bivariate t, polar coordinators
Subjects: Q Science > QA Mathematics
Divisions: University Structure - Pre August 2011 > Southampton Statistical Sciences Research Institute
ePrint ID: 55204
Date Deposited: 05 Aug 2008
Last Modified: 27 Mar 2014 18:38
URI: http://eprints.soton.ac.uk/id/eprint/55204

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