An independence point method of confidence band construction for multiple linear regression models
An independence point method of confidence band construction for multiple linear regression models
This article addresses the problem of confidence band construction for a standard multiple linear regression model. An “independence point” method of construction is developed which generalizes the method of Gafarian (1964) for a simple linear regression model to a multiple linear regression model. Wynn (1984) pioneered the approach of basing confidence bands for a polynomial regression on a set of nodes where the function estimates are independent, and this approach is exploited in this article. This method requires only critical points from t-distributions so that the confidence bands are easy to construct. Both one-sided and two-sided confidence bands can be constructed using this method. An illustration of the new method is provided, and comparisons are made with other procedures
confidence bands, independence points, kimball's inequality, multiple linear regression, t-distribution
4132-4141
Hayter, A.J.
55bd07a5-db1d-4d3d-8c87-b307485420d9
Kiatsupaibul, S.
b072063d-4be1-4ca0-8d4f-27740f0fa651
Liu, W.
b64150aa-d935-4209-804d-24c1b97e024a
Wynn, H.P.
849f3bf7-a005-4361-a9ec-f3a28b75d398
27 September 2012
Hayter, A.J.
55bd07a5-db1d-4d3d-8c87-b307485420d9
Kiatsupaibul, S.
b072063d-4be1-4ca0-8d4f-27740f0fa651
Liu, W.
b64150aa-d935-4209-804d-24c1b97e024a
Wynn, H.P.
849f3bf7-a005-4361-a9ec-f3a28b75d398
Hayter, A.J., Kiatsupaibul, S., Liu, W. and Wynn, H.P.
(2012)
An independence point method of confidence band construction for multiple linear regression models.
Communications in Statistics: Theory and Methods, 41 (22), .
(doi:10.1080/03610926.2011.569679).
Abstract
This article addresses the problem of confidence band construction for a standard multiple linear regression model. An “independence point” method of construction is developed which generalizes the method of Gafarian (1964) for a simple linear regression model to a multiple linear regression model. Wynn (1984) pioneered the approach of basing confidence bands for a polynomial regression on a set of nodes where the function estimates are independent, and this approach is exploited in this article. This method requires only critical points from t-distributions so that the confidence bands are easy to construct. Both one-sided and two-sided confidence bands can be constructed using this method. An illustration of the new method is provided, and comparisons are made with other procedures
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Accepted/In Press date: 28 February 2011
Published date: 27 September 2012
Keywords:
confidence bands, independence points, kimball's inequality, multiple linear regression, t-distribution
Organisations:
Mathematical Sciences
Identifiers
Local EPrints ID: 381039
URI: http://eprints.soton.ac.uk/id/eprint/381039
ISSN: 0361-0926
PURE UUID: b0972ff8-2907-4884-b636-37a7323eb826
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Date deposited: 24 Sep 2015 09:04
Last modified: 15 Mar 2024 02:43
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Contributors
Author:
A.J. Hayter
Author:
S. Kiatsupaibul
Author:
H.P. Wynn
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