This paper fills this gap by studying one particular simultaneous confidence band for multivariate linear regression. Because of the shape of the band, the word 'tube' is more pertinent and so will be used to replace the word 'band'. It is shown that the construction of the tube is ...
In linear models, it is known that that the sup‐t confidence band is narrower than commonly used alternatives—for example, Bonferroni and projection bands. We show that the same ranking applies asymptotically even in general nonlinear models, such as vector autoregressions (VARs). Moreover, we...
A smooth simultaneous confidence band (SCB) is then constructed based on the proposed smooth distribution estimator and Kolmogorov distribution. Simulation examples support the asymptotic theory.doi:10.1214/13-AOS1197Wang, JiangyanLiu, RongCheng, Fuxia...
Then, using an existing confidence region about the parameters of a nonlinear regression model and the maximization and minimization procedure, a generally conservative simultaneous confidence band is constructed about the model. Two examples are given, and some problems with the procedure are discussed...
Song Q, Liu R, Shao Q, Yang L (2014) A simultaneous confidence band for dense longitudinal regression. Commun Stat Theory Methods 43:5195–5210 MathSciNet MATHQ. Song, R. Liu, Q. Shao, and L. Yang. A simultaneous confidence band for dense longitudinal regression. Communications in ...
Comparison between the hyperbolic and constant width bands is then addressed under both the average width and minimum volume confidence set criteria. It is observed that the constant width band can be drastically less efficient than the hyperbolic band when k>1. Finally it is pointed out how the...
The asymptotic distribution of the maximal deviation between the estimator and the true regression function is derived and an asymptotically accurate simultaneous confidence band is constructed. The estimator for the regression function is shown to be oracally efficient in the sense that it is uniformly...
北京大学数学学士(1987),美国北卡罗来纳大学教堂山分校统计学博士(1995),美国密西根州立大学统计系终身正教授(2006-2014),研究生主任(2007-2010)。国际统计学院当选会员(Elected Member, International Statistical Institute ISI),美国统计协会当选会士(Elected Fellow, American Statistical Association ASA),国际数理统计...
Erratum to “Simultaneous confidence band for the difference of segmented linear models” [Journal of Statistical Planning and Inference 141 (2) (February) (2011) 1059–1068]Publication » Erratum to “Simultaneous confidence band for the difference of segmented linear models” [Journal of ...
Confidence intervals having this property are characterized and the Working–Hotelling band is discussed with reference to it. It is shown how this band may be sharpened to give exact confidence levels in linear and quadratic regression. Tables are given from which the confidence bands may be ...