Statistical inferences for linear regression models when the covariates have functional relationships: polynomial regression
Statistical inferences for linear regression models when the covariates have functional relationships: polynomial regression
In many linear regression models, there are functional relationships among the covariates. The usual (partial) F tests for these models do not utilize these functional relationships, however, and so have certain undesirable properties. Improvements over these F tests are proposed in this article, and they are based on simultaneous confidence bands. For ease of illustration of the ideas, we focus on the polynomial regression model.
confidence bands, F tests, linear regression, polynomial regression, simultaneous inference, statistical simulation
315-324
Liu, Wei
b64150aa-d935-4209-804d-24c1b97e024a
Wynn, H.P.
849f3bf7-a005-4361-a9ec-f3a28b75d398
Hayter, A.J.
55bd07a5-db1d-4d3d-8c87-b307485420d9
12 June 2008
Liu, Wei
b64150aa-d935-4209-804d-24c1b97e024a
Wynn, H.P.
849f3bf7-a005-4361-a9ec-f3a28b75d398
Hayter, A.J.
55bd07a5-db1d-4d3d-8c87-b307485420d9
Liu, Wei, Wynn, H.P. and Hayter, A.J.
(2008)
Statistical inferences for linear regression models when the covariates have functional relationships: polynomial regression.
Journal of Statistical Computation and Simulation, 78 (4), .
(doi:10.1080/00949650601100981).
Abstract
In many linear regression models, there are functional relationships among the covariates. The usual (partial) F tests for these models do not utilize these functional relationships, however, and so have certain undesirable properties. Improvements over these F tests are proposed in this article, and they are based on simultaneous confidence bands. For ease of illustration of the ideas, we focus on the polynomial regression model.
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Published date: 12 June 2008
Keywords:
confidence bands, F tests, linear regression, polynomial regression, simultaneous inference, statistical simulation
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Local EPrints ID: 55191
URI: http://eprints.soton.ac.uk/id/eprint/55191
ISSN: 0094-9655
PURE UUID: 967a6827-5f9f-44e4-926e-a37689157233
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Date deposited: 05 Aug 2008
Last modified: 16 Mar 2024 02:42
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Author:
H.P. Wynn
Author:
A.J. Hayter
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