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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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.
|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
|Date Deposited:||05 Aug 2008|
|Last Modified:||01 Jun 2011 09:35|
|Contact Email Address:||W.Liu@maths.soton.ac.uk|
|RDF:||RDF+N-Triples, RDF+N3, RDF+XML, Browse.|
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