Simultaneous confidence bands for all contrasts of three or more simple linear regression models over an interval
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 (-[infinity],[infinity]) 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.
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- Wei Liu & Shan Lin & Walter W. Piegorsch, 2008. "Construction of Exact Simultaneous Confidence Bands for a Simple Linear Regression Model," International Statistical Review, International Statistical Institute, vol. 76(1), pages 39-57, 04.
- Liu W. & Jamshidian M. & Zhang Y., 2004. "Multiple Comparison of Several Linear Regression Models," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 395-403, January.
- Walter W. Piegorsch & R. Webster West & Wei Pan & Ralph L. Kodell, 2005. "Low dose risk estimation via simultaneous statistical inferences," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 54(1), pages 245-258.
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