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Activity Number:
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116
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Type:
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Contributed
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Date/Time:
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Monday, August 9, 2004 : 10:30 AM to 12:20 PM
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Sponsor:
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General Methodology
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| Abstract - #301217 |
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Title:
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Simultaneous Confidence Bands in Regression with Constrained Predictors
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Author(s):
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Mortaza Jamshidian*+ and Wei Liu and Ying Zhang and Johnathan Donnelly
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Companies:
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California State University, Fullerton and University of Southampton and University of Central Florida and University of Southampton
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Address:
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Mathematics Dept., Fullerton, CA, 92834,
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Keywords:
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linear regression ; simultaneous confidence bands ; statistical simulation
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Abstract:
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This article presents a method for the construction of a simultaneous confidence band for the normal-error multiple linear regression model. The confidence bands considered have their width proportional to the standard error of the estimated regression function, and the predictor variables are allowed to be constrained in intervals. Published papers in this area give exact bands only for the simple regression model. When there is more than one predictor variable, only conservative bands are proposed in the statistics literature. This paper advances this methodology by providing exact confidence bands for regression models with any number of predictor variables. Additionally, a criterion is proposed to assess the sensitivity of a simultaneous confidence band. This criterion is defined to be the probability that a false linear regression model is excluded from the band at least at one point and hence this false linear regression model is correctly declared as a false model by the band. Finally, the paper discusses computational algorithms for obtaining the confidence band.
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