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

Wei Liu, Shan Lin, Walter W. Piegorsch

Research output: Contribution to journalArticle

24 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)39-57
Number of pages19
JournalInternational Statistical Review
Volume76
Issue number1
DOIs
StatePublished - Apr 1 2008

Keywords

  • Bivariate normal
  • Bivariate t
  • Polar coordinators
  • Simple linear regression
  • Simultaneous inferences

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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