Simultaneous confidence bands for all contrasts of three or more simple linear regression models over an interval


Jamshidian, Mortaza, Liu, Wei and Bretz, Frank (2010) Simultaneous confidence bands for all contrasts of three or more simple linear regression models over an interval. Computational Statistics & Data Analysis, 54, (6), 1475-1483. (doi:10.1016/j.csda.2010.01.022 ).

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Description/Abstract

Simultaneous confidence intervals are used in Scheffé (1953) to assess any contrasts of several normal means. In this paper, the problem of assessing any contrasts of several simple linear regression models by using simultaneous confidence bands is considered. Using numerical integration, Spurrier (1999) constructed exact simultaneous confidence bands for all the contrasts of several regression lines over the whole range (−∞,∞) of the explanatory variable when the design matrices of the regression lines are all equal. In this paper, a simulation-based method is proposed to construct simultaneous confidence bands for all the contrasts of the regression lines when the explanatory variable is restricted to an interval and the design matrices of the regression lines may be different. The critical value calculated by this method can be as close to the exact critical value as required if the number of replications in the simulation is chosen sufficiently large. The methodology is illustrated with a real problem in which sizes of the left atrium of infants in three diagnostic groups (severely impaired, mildly impaired and normal) are compared

Item Type: Article
ISSNs: 0167-9473
Keywords: comparing groups, comparison of regression lines, simultaneous inferences, size of atrium in infants, statistical simulation
Subjects: H Social Sciences > HA Statistics
Q Science > QA Mathematics
Divisions: University Structure - Pre August 2011 > School of Mathematics > Statistics
ePrint ID: 176555
Date Deposited: 09 Mar 2011 09:01
Last Modified: 28 Mar 2014 15:25
Research Funder: EPSRC
Projects:
Construction and Applications of Simultaneous Confidence Bands for Linear Regression Models
Funded by: EPSRC (EP/E046126/1)
Led by: Wei Liu
20 July 2007 to 19 October 2007
URI: http://eprints.soton.ac.uk/id/eprint/176555

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