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September, 1986 Conservative Confidence Bands in Curvilinear Regression
Daniel Q. Naiman
Ann. Statist. 14(3): 896-906 (September, 1986). DOI: 10.1214/aos/1176350040

Abstract

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 $S^{k-1}$.

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Daniel Q. Naiman. "Conservative Confidence Bands in Curvilinear Regression." Ann. Statist. 14 (3) 896 - 906, September, 1986. https://doi.org/10.1214/aos/1176350040

Information

Published: September, 1986
First available in Project Euclid: 12 April 2007

zbMATH: 0607.62077
MathSciNet: MR856796
Digital Object Identifier: 10.1214/aos/1176350040

Subjects:
Primary: 60E15
Secondary: 60D05, 62F25, 62J02, 62J05

Rights: Copyright © 1986 Institute of Mathematical Statistics

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Vol.14 • No. 3 • September, 1986
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