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March, 1988 Confidence Regions in Multivariate Calibration
Samuel D. Oman
Ann. Statist. 16(1): 174-187 (March, 1988). DOI: 10.1214/aos/1176350698

Abstract

The multivariate calibration problem is considered, in which a sample of $n$ observations on vectors $\xi_{(i)}$ (of "true values") and $Y_{(i)}$ (of less accurate but more easily obtained values) are to be used to estimate the unknown $\xi$ corresponding to a future $Y$. It is assumed that $Y = BX + \varepsilon$, where $\varepsilon$ is multivariate normal and $X = h(\xi)$ for known $h$. Current methods for obtaining a confidence region $C$ for $\xi$, which consist of computing a region $R$ for $X$ and then taking $C = h^{-1}(R)$, have the disadvantage that although the region $R$ might be nicely behaved, the region $C$ need not be. An alternative method is proposed which gives a well-behaved region (corresponding to the uniformly most accurate translation-invariant region when $h$ is linear, $B$ is known and the covariance matrix of $\varepsilon$ is a known multiple of the identity). An application is given to the estimation of gestational age using ultrasound fetal bone measurements.

Citation

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Samuel D. Oman. "Confidence Regions in Multivariate Calibration." Ann. Statist. 16 (1) 174 - 187, March, 1988. https://doi.org/10.1214/aos/1176350698

Information

Published: March, 1988
First available in Project Euclid: 12 April 2007

zbMATH: 0637.62033
MathSciNet: MR924864
Digital Object Identifier: 10.1214/aos/1176350698

Subjects:
Primary: 62F25
Secondary: 62H99

Rights: Copyright © 1988 Institute of Mathematical Statistics

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Vol.16 • No. 1 • March, 1988
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