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Shrinkage estimation and the use of additional information when calibrating in the presence of random effects
Author(s) -
Oman Samuel D.
Publication year - 2013
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.5846
Subject(s) - estimator , calibration , context (archaeology) , mathematics , confidence interval , set (abstract data type) , statistics , point (geometry) , point estimation , value (mathematics) , algorithm , sampling (signal processing) , data set , computer science , geometry , paleontology , filter (signal processing) , computer vision , biology , programming language
Let x denote a precise measurement of a quantity and Y an inexact measurement, which is, however, less expensive or more easily obtained than x . We have available a calibration set comprising clustered sets of ( x , Y ) observations, obtained from different sampling units. At the prediction step, we will only observe Y for a new unit, and we wish to estimate the corresponding unknown x , which we denote by ξ . This problem has been treated under the assumption that x and Y are linearly related. Here, we expand on those results in three directions: First, we show that if we center ξ about a known value c , for example, the mean x ‐value of the calibration set, then the proposed estimator now shrinks to c . Second, we examine in detail the performance of the estimator, which was proposed when one or more ( x , Y ) observations can be obtained for the new subject. Third, we compare the Fieller‐like confidence intervals, previously proposed, with t ‐like intervals based on asymptotic moments of the point estimate. We illustrate and evaluate our procedures in the context of a data set of true bladder‐volumes ( x ) and ultrasound measurements ( Y ). Copyright © 2013 John Wiley & Sons, Ltd.