Comparison of hyperbolic and constant width simultaneous confidence bands in multiple linear regression under MVCS criterion

W. Liu, A. J. Hayter, Walter W Piegorsch, P. Ah-Kine

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

A simultaneous confidence band provides useful information on the plausible range of the unknown regression model, and different confidence bands can often be constructed for the same regression model. For a simple regression line, Liu and Hayter [W. Liu, A.J. Hayter, Minimum area confidence set optimality for confidence bands in simple linear regression, J. Amer. Statist. Assoc. 102 (477) (2007) pp. 181-190] proposed the use of the area of the confidence set corresponding to a confidence band as an optimality criterion in comparison of confidence bands; the smaller the area of the confidence set, the better the corresponding confidence band. This minimum area confidence set (MACS) criterion can be generalized to a minimum volume confidence set (MVCS) criterion in the study of confidence bands for a multiple linear regression model. In this paper hyperbolic and constant width confidence bands for a multiple linear regression model over a particular ellipsoidal region of the predictor variables are compared under the MVCS criterion. It is observed that whether one band is better than the other depends on the magnitude of one particular angle that determines the size of the predictor variable region. When the angle and hence the size of the predictor variable region is small, the constant width band is better than the hyperbolic band but only marginally. When the angle and hence the size of the predictor variable region is large the hyperbolic band can be substantially better than the constant width band. Crown

Original languageEnglish (US)
Pages (from-to)1432-1439
Number of pages8
JournalJournal of Multivariate Analysis
Volume100
Issue number7
DOIs
StatePublished - Aug 2009

Fingerprint

Simultaneous Confidence Bands
Confidence Set
Confidence Bands
Multiple Linear Regression
Linear regression
Predictors
Linear Regression Model
Angle
Regression Model
Bandwidth
Regression line
Simple Linear Regression
Optimality Criteria
Multiple linear regression
Confidence set
Confidence
Optimality
Unknown

Keywords

  • Confidence sets
  • Linear regression
  • Simultaneous confidence bands
  • Statistical inference

ASJC Scopus subject areas

  • Statistics, Probability and Uncertainty
  • Numerical Analysis
  • Statistics and Probability

Cite this

Comparison of hyperbolic and constant width simultaneous confidence bands in multiple linear regression under MVCS criterion. / Liu, W.; Hayter, A. J.; Piegorsch, Walter W; Ah-Kine, P.

In: Journal of Multivariate Analysis, Vol. 100, No. 7, 08.2009, p. 1432-1439.

Research output: Contribution to journalArticle

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