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