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

Record type: Monograph (Working Paper)

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 (2007) propose 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 so 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 so 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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Citation

Liu, W., Hayter, A.J., Piegorsch, W.W. and Ah-Kine, P. (2008) Comparison of hyperbolic and constant width simultaneous confidence bands in multiple linear regression under MVCS criterion , Southampton, UK Southampton Statistical Sciences Research Institute 13pp. (Methodology Working Papers, M08/08).

More information

Submitted date: 21 October 2008
Keywords: confidence sets, linear regression, simultaneous confidence bands, statistical inference

Identifiers

Local EPrints ID: 63618
URI: http://eprints.soton.ac.uk/id/eprint/63618
PURE UUID: 0b695e60-b7e6-42fb-83bf-74323ab178b9
ORCID for W. Liu: ORCID iD orcid.org/0000-0002-4719-0345

Catalogue record

Date deposited: 21 Oct 2008
Last modified: 17 Jul 2017 14:16

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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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