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March, 1990 Nonparametric Estimation of Optimal Performance Criteria in Quality Engineering
R. J. Carroll, Peter Hall
Ann. Statist. 18(1): 281-302 (March, 1990). DOI: 10.1214/aos/1176347501


Box and Leon, Shoemaker and Kackar have discussed the problem of closeness to target in quality engineering. If the mean response $f(x, z)$ depends on $(x, z)$, the variance function is a PERMIA if it is $g(z)$, i.e., depends only on $z$. The goal is to find $(x_0, z_0)$ which minimizes variance while achieving a target mean value. We pose and answer the question: For given smoothness assumptions about $f$ and $g$, how accurately can we estimate $x_0$ and $z_0$? As part of the investigation, we also find optimal rates of convergence for estimating $f, g$ and their derivatives.


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R. J. Carroll. Peter Hall. "Nonparametric Estimation of Optimal Performance Criteria in Quality Engineering." Ann. Statist. 18 (1) 281 - 302, March, 1990.


Published: March, 1990
First available in Project Euclid: 12 April 2007

zbMATH: 0763.62020
MathSciNet: MR1041394
Digital Object Identifier: 10.1214/aos/1176347501

Primary: 62G05
Secondary: 62G20

Rights: Copyright © 1990 Institute of Mathematical Statistics


Vol.18 • No. 1 • March, 1990
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