Confidence regions in multivariate calibration
type: Item
instance of: scholarly article
title: Confidence regions in multivariate calibration
zbMATH Open document ID: 0637.62033
author: Samuel D. Oman
published in: The Annals of Statistics
publication date: 1988-01-01T00:00:00Z
review text: 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 \(Y=BX+\epsilon\), where \(\epsilon\) 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 \(\epsilon\) is a known multiple of the identity). An application is given to the estimation of gestational age using ultrasound fetal bone measurements.
Mathematics Subject Classification ID: 62F25
Mathematics Subject Classification ID: 62H99
Mathematics Subject Classification ID: 62P10
Mathematics Subject Classification ID: 62J05
Mathematics Subject Classification ID: 62J99
Mathematics Subject Classification ID: 62H12
zbMATH DE Number: 4039019
zbMATH Keywords: multivariate calibration problem
zbMATH Keywords: multivariate normal
zbMATH Keywords: confidence region
zbMATH Keywords: uniformly most accurate translation-invariant region
zbMATH Keywords: estimation of gestational age
zbMATH Keywords: ultrasound fetal bone measurements
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aos/1176350698
OpenAlex ID: W1985041398
DOI: 10.1214/AOS/1176350698
description: scientific article; zbMATH DE number 4039019