An Independence Point Method of Confidence Band Construction for Multiple Linear Regression Models |
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Authors: | A. J. Hayter S. Kiatsupaibul W. Liu H. P. Wynn |
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Affiliation: | 1. Department of Statistics and Operations Technology , University of Denver , Denver , Colorado , USA Anthony.Hayter@du.edu;3. Department of Statistics , Chulalongkorn University , Bangkok , Thailand;4. S3RI and School of Mathematics , University of Southampton , Southampton , United Kingdom;5. Department of Statistics , London School of Economics , London , United Kingdom |
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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 Wynn , H. P. ( 1984 ). An exact confidence band for one-dimensional polynomial regression . Biometrika 71 : 375 – 9 .[Crossref], [Web of Science ®] , [Google Scholar]) 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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Keywords: | Confidence bands Independence points Kimball's inequality Multiple linear regression t-distribution |
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