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

Wei Liu, Shan Lin, Walter W Piegorsch

Research output: Contribution to journalArticle

23 Citations (Scopus)

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 2008

Fingerprint

Simultaneous Confidence Bands
Simple Linear Regression
Linear Regression Model
Confidence Bands
Polar coordinates
Coordinate Transformation
Random Vector
Sun
Linear regression
Regression Model
Bandwidth
Statistics
Unknown
Linear regression model
Confidence

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)
  • Statistics and Probability

Cite this

Construction of exact simultaneous confidence bands for a simple linear regression model. / Liu, Wei; Lin, Shan; Piegorsch, Walter W.

In: International Statistical Review, Vol. 76, No. 1, 04.2008, p. 39-57.

Research output: Contribution to journalArticle

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