Abstract
A simultaneous confidence band provides useful information on the plausible range of the unknown regression model, and different confidence bands can often be constructed for the same regression model. For a simple regression line, Liu and Hayter [W. Liu, A.J. Hayter, Minimum area confidence set optimality for confidence bands in simple linear regression, J. Amer. Statist. Assoc. 102 (477) (2007) pp. 181-190] proposed the use of the area of the confidence set corresponding to a confidence band as an optimality criterion in comparison of confidence bands; the smaller the area of the confidence set, the better the corresponding confidence band. This minimum area confidence set (MACS) criterion can be generalized to a minimum volume confidence set (MVCS) criterion in the study of confidence bands for a multiple linear regression model. In this paper hyperbolic and constant width confidence bands for a multiple linear regression model over a particular ellipsoidal region of the predictor variables are compared under the MVCS criterion. It is observed that whether one band is better than the other depends on the magnitude of one particular angle that determines the size of the predictor variable region. When the angle and hence the size of the predictor variable region is small, the constant width band is better than the hyperbolic band but only marginally. When the angle and hence the size of the predictor variable region is large the hyperbolic band can be substantially better than the constant width band. Crown
| Original language | English (US) |
|---|---|
| Pages (from-to) | 1432-1439 |
| Number of pages | 8 |
| Journal | Journal of Multivariate Analysis |
| Volume | 100 |
| Issue number | 7 |
| DOIs | |
| State | Published - Aug 2009 |
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Keywords
- Confidence sets
- Linear regression
- Simultaneous confidence bands
- Statistical inference
ASJC Scopus subject areas
- Statistics, Probability and Uncertainty
- Numerical Analysis
- Statistics and Probability
Cite this
Comparison of hyperbolic and constant width simultaneous confidence bands in multiple linear regression under MVCS criterion. / Liu, W.; Hayter, A. J.; Piegorsch, Walter W; Ah-Kine, P.
In: Journal of Multivariate Analysis, Vol. 100, No. 7, 08.2009, p. 1432-1439.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Comparison of hyperbolic and constant width simultaneous confidence bands in multiple linear regression under MVCS criterion
AU - Liu, W.
AU - Hayter, A. J.
AU - Piegorsch, Walter W
AU - Ah-Kine, P.
PY - 2009/8
Y1 - 2009/8
N2 - A simultaneous confidence band provides useful information on the plausible range of the unknown regression model, and different confidence bands can often be constructed for the same regression model. For a simple regression line, Liu and Hayter [W. Liu, A.J. Hayter, Minimum area confidence set optimality for confidence bands in simple linear regression, J. Amer. Statist. Assoc. 102 (477) (2007) pp. 181-190] proposed the use of the area of the confidence set corresponding to a confidence band as an optimality criterion in comparison of confidence bands; the smaller the area of the confidence set, the better the corresponding confidence band. This minimum area confidence set (MACS) criterion can be generalized to a minimum volume confidence set (MVCS) criterion in the study of confidence bands for a multiple linear regression model. In this paper hyperbolic and constant width confidence bands for a multiple linear regression model over a particular ellipsoidal region of the predictor variables are compared under the MVCS criterion. It is observed that whether one band is better than the other depends on the magnitude of one particular angle that determines the size of the predictor variable region. When the angle and hence the size of the predictor variable region is small, the constant width band is better than the hyperbolic band but only marginally. When the angle and hence the size of the predictor variable region is large the hyperbolic band can be substantially better than the constant width band. Crown
AB - A simultaneous confidence band provides useful information on the plausible range of the unknown regression model, and different confidence bands can often be constructed for the same regression model. For a simple regression line, Liu and Hayter [W. Liu, A.J. Hayter, Minimum area confidence set optimality for confidence bands in simple linear regression, J. Amer. Statist. Assoc. 102 (477) (2007) pp. 181-190] proposed the use of the area of the confidence set corresponding to a confidence band as an optimality criterion in comparison of confidence bands; the smaller the area of the confidence set, the better the corresponding confidence band. This minimum area confidence set (MACS) criterion can be generalized to a minimum volume confidence set (MVCS) criterion in the study of confidence bands for a multiple linear regression model. In this paper hyperbolic and constant width confidence bands for a multiple linear regression model over a particular ellipsoidal region of the predictor variables are compared under the MVCS criterion. It is observed that whether one band is better than the other depends on the magnitude of one particular angle that determines the size of the predictor variable region. When the angle and hence the size of the predictor variable region is small, the constant width band is better than the hyperbolic band but only marginally. When the angle and hence the size of the predictor variable region is large the hyperbolic band can be substantially better than the constant width band. Crown
KW - Confidence sets
KW - Linear regression
KW - Simultaneous confidence bands
KW - Statistical inference
UR - http://www.scopus.com/inward/record.url?scp=64249157647&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=64249157647&partnerID=8YFLogxK
U2 - 10.1016/j.jmva.2008.12.003
DO - 10.1016/j.jmva.2008.12.003
M3 - Article
AN - SCOPUS:64249157647
VL - 100
SP - 1432
EP - 1439
JO - Journal of Multivariate Analysis
JF - Journal of Multivariate Analysis
SN - 0047-259X
IS - 7
ER -