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Simultaneous confidence bands for a percentile line in linear regression

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Simultaneous confidence bands for a percentile line in linear regression. / Han, Yang; Liu, Wei; Bretz, Frank et al.
In: Computational Statistics and Data Analysis, Vol. 81, 01.2015, p. 1-9.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Han, Y, Liu, W, Bretz, F & Wan, F 2015, 'Simultaneous confidence bands for a percentile line in linear regression', Computational Statistics and Data Analysis, vol. 81, pp. 1-9. https://doi.org/10.1016/j.csda.2014.07.009

APA

Han, Y., Liu, W., Bretz, F., & Wan, F. (2015). Simultaneous confidence bands for a percentile line in linear regression. Computational Statistics and Data Analysis, 81, 1-9. https://doi.org/10.1016/j.csda.2014.07.009

Vancouver

Han Y, Liu W, Bretz F, Wan F. Simultaneous confidence bands for a percentile line in linear regression. Computational Statistics and Data Analysis. 2015 Jan;81:1-9. Epub 2014 Jul 23. doi: 10.1016/j.csda.2014.07.009

Author

Han, Yang ; Liu, Wei ; Bretz, Frank et al. / Simultaneous confidence bands for a percentile line in linear regression. In: Computational Statistics and Data Analysis. 2015 ; Vol. 81. pp. 1-9.

Bibtex

@article{d98a21a48e6446a19d1ea12dc35d34fa,
title = "Simultaneous confidence bands for a percentile line in linear regression",
abstract = "Construction of simultaneous confidence bands for a percentile line in linear regression has been considered by several authors. But only conservative symmetric bands, which use critical constants over the whole covariate range (−∞,∞), are available in the literature. New methods allow the construction of exact symmetric bands for a percentile line over a finite interval of the covariate x. The exact symmetric bands can be substantially narrower than the corresponding conservative symmetric bands. Several exact symmetric confidence bands are compared under the average band width criterion. Furthermore, new asymmetric confidence bands for a percentile line are proposed. They are uniformly and can be very substantially narrower than the corresponding exact symmetric bands. Therefore, asymmetric bands should always be used under the average band width criterion. The proposed methods are illustrated with a real example.",
keywords = "Confidence level, Linear regression, Percentile line, Simultaneous confidence band, Statistical simulation",
author = "Yang Han and Wei Liu and Frank Bretz and Fang Wan",
year = "2015",
month = jan,
doi = "10.1016/j.csda.2014.07.009",
language = "English",
volume = "81",
pages = "1--9",
journal = "Computational Statistics and Data Analysis",
issn = "0167-9473",
publisher = "Elsevier",

}

RIS

TY - JOUR

T1 - Simultaneous confidence bands for a percentile line in linear regression

AU - Han, Yang

AU - Liu, Wei

AU - Bretz, Frank

AU - Wan, Fang

PY - 2015/1

Y1 - 2015/1

N2 - Construction of simultaneous confidence bands for a percentile line in linear regression has been considered by several authors. But only conservative symmetric bands, which use critical constants over the whole covariate range (−∞,∞), are available in the literature. New methods allow the construction of exact symmetric bands for a percentile line over a finite interval of the covariate x. The exact symmetric bands can be substantially narrower than the corresponding conservative symmetric bands. Several exact symmetric confidence bands are compared under the average band width criterion. Furthermore, new asymmetric confidence bands for a percentile line are proposed. They are uniformly and can be very substantially narrower than the corresponding exact symmetric bands. Therefore, asymmetric bands should always be used under the average band width criterion. The proposed methods are illustrated with a real example.

AB - Construction of simultaneous confidence bands for a percentile line in linear regression has been considered by several authors. But only conservative symmetric bands, which use critical constants over the whole covariate range (−∞,∞), are available in the literature. New methods allow the construction of exact symmetric bands for a percentile line over a finite interval of the covariate x. The exact symmetric bands can be substantially narrower than the corresponding conservative symmetric bands. Several exact symmetric confidence bands are compared under the average band width criterion. Furthermore, new asymmetric confidence bands for a percentile line are proposed. They are uniformly and can be very substantially narrower than the corresponding exact symmetric bands. Therefore, asymmetric bands should always be used under the average band width criterion. The proposed methods are illustrated with a real example.

KW - Confidence level

KW - Linear regression

KW - Percentile line

KW - Simultaneous confidence band

KW - Statistical simulation

U2 - 10.1016/j.csda.2014.07.009

DO - 10.1016/j.csda.2014.07.009

M3 - Journal article

VL - 81

SP - 1

EP - 9

JO - Computational Statistics and Data Analysis

JF - Computational Statistics and Data Analysis

SN - 0167-9473

ER -