Comparison of hyperbolic and constant width simultaneous confidence bands in multiple linear regression under MVCS criterion
Comparison of hyperbolic and constant width simultaneous confidence bands in multiple linear regression under MVCS criterion
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.
confidence sets, linear regression, simultaneous confidence bands, statistical inference
Southampton Statistical Sciences Research Institute, University of Southampton
Liu, W.
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Hayter, A.J.
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Piegorsch, W.W.
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Ah-Kine, P.
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Liu, W.
b64150aa-d935-4209-804d-24c1b97e024a
Hayter, A.J.
55bd07a5-db1d-4d3d-8c87-b307485420d9
Piegorsch, W.W.
cd71e12f-98d4-42a4-baaa-650528eea7c9
Ah-Kine, P.
2553d7c8-99b4-492f-95ef-43c68e109737
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
(Methodology Working Papers, M08/08)
Southampton, UK.
Southampton Statistical Sciences Research Institute, University of Southampton
13pp.
(Submitted)
Record type:
Monograph
(Working Paper)
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 (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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63618-01.pdf
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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
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Date deposited: 21 Oct 2008
Last modified: 16 Mar 2024 02:42
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Contributors
Author:
A.J. Hayter
Author:
W.W. Piegorsch
Author:
P. Ah-Kine
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