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

Liu, W., Hayter, A.J., Piegorsch, W.W. and Ah-Kine, P. (2009) Comparison of hyperbolic and constant width simultaneous confidence bands in multiple linear regression under MVCS criterion Journal of Multivariate Analysis, 100, (7), pp. 1432-1439. (doi:10.1016/j.jmva.2008.12.003).

Record type: Article

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.

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More information

e-pub ahead of print date: 16 December 2008
Published date: August 2009
Keywords: confidence sets, linear regression, simultaneous confidence bands, statistical inference
Organisations: Statistics

Identifiers

Local EPrints ID: 146029
URI: http://eprints.soton.ac.uk/id/eprint/146029
ISSN: 0047-259X
PURE UUID: 1b6ca6f0-d136-4914-8150-1967547d40d2
ORCID for W. Liu: ORCID iD orcid.org/0000-0002-4719-0345

Catalogue record

Date deposited: 20 Apr 2010 11:57
Last modified: 18 Jul 2017 23:05

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Contributors

Author: W. Liu ORCID iD
Author: A.J. Hayter
Author: W.W. Piegorsch
Author: P. Ah-Kine

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