A ray method of confidence band construction for multiple linear regression models

This paper addresses the problem of confidence band construction for a standard multiple linear regression model. A “ray” method of construction is developed which generalizes the method of Graybill and Bowden [1967. Linear segment confidence bands for simple linear regression models. J. Amer. Stati...

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Bibliographic Details
Published in:Journal of statistical planning and inference 2009-02, Vol.139 (2), p.329-334
Main Authors: Hayter, A.J., Liu, W., Ah-Kine, P.
Format: Article
Language:English
Subjects:
Confidence bands
Distribution theory
Exact sciences and technology
General topics
Linear inference, regression
Mathematical analysis
Mathematics
Multiple linear regression
Partial differential equations
Probability and statistics
Probability theory and stochastic processes
Sciences and techniques of general use
Statistics
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Summary:This paper addresses the problem of confidence band construction for a standard multiple linear regression model. A “ray” method of construction is developed which generalizes the method of Graybill and Bowden [1967. Linear segment confidence bands for simple linear regression models. J. Amer. Statist. Assoc. 62, 403–408] for a simple linear regression model to a multiple linear regression model. By choosing suitable directions for the rays 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.
ISSN:0378-3758
1873-1171
DOI:10.1016/j.jspi.2008.04.029