This paper gives a method for constructing conservative Scheffe-type simultaneous confidence bands for curvilinear regression functions over finite intervals. The method is based on the use of a geometric inequality giving an upper bound for the uniform measure of the set of points within a given distance from y, an arbitrary piecewise differentiable path with finite length in $S^{k-1}$, the unit sphere in $R^k$. The upper bound is obtained by "straightening" the path so that it lies in a great circle in $S^{k-1}$.
@article{1176350040,
author = {Naiman, Daniel Q.},
title = {Conservative Confidence Bands in Curvilinear Regression},
journal = {Ann. Statist.},
volume = {14},
number = {2},
year = {1986},
pages = { 896-906},
language = {en},
url = {http://dml.mathdoc.fr/item/1176350040}
}
Naiman, Daniel Q. Conservative Confidence Bands in Curvilinear Regression. Ann. Statist., Tome 14 (1986) no. 2, pp. 896-906. http://gdmltest.u-ga.fr/item/1176350040/