A comparison of location estimators for interlaboratory data contaminated with value and uncertainty outliers
 David Lee Duewer
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While estimation of measurement uncertainty (MU) is increasingly acknowledged as an essential component of the chemical measurement process, there is little agreement on how best to use even nominally wellestimated MU. There are philosophical and practical issues involved in defining what is “best” for a given data set; however, there is remarkably little guidance on how well different MUusing estimators perform with imperfect data. This report characterizes the bias, efficiency, and robustness properties for several commonly used or recently proposed estimators of true location, μ, using “Monte Carlo” (MC) evaluation of “measurement” data sets drawn from welldefined distributions. These synthetic models address a number of issues pertinent to interlaboratory comparisons studies. While the MC results do not provide specific guidance on “which estimator is best” for any given set of real data, they do provide broad insight into the expected relative performance within broadly defined scenarios. Perhaps the broadest and most emphatic guidance from the present study is that (1) wellestimated measurement uncertainties can be used to improve the reliability of location determination and (2) some approaches to using measurement uncertainties are better than others. The traditional inverse squared uncertaintyweighted estimators perform well only in the absence of unrepresentative values (value outliers) or underestimated uncertainties (uncertainty outliers); even modest contamination by such outliers may result in relatively inaccurate estimates. In contrast, some inverse total varianceweightedestimators and probability density function areabased estimators perform well for all scenarios evaluated, including underestimated uncertainties, extreme value outliers, and asymmetric contamination.
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 Title
 A comparison of location estimators for interlaboratory data contaminated with value and uncertainty outliers
 Journal

Accreditation and Quality Assurance
Volume 13, Issue 45 , pp 193216
 Cover Date
 20080501
 DOI
 10.1007/s0076900803603
 Print ISSN
 09491775
 Online ISSN
 14320517
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 Consensus value
 Interlaboratory comparisons
 Measurement uncertainty
 Mixture models
 Monte Carlo evaluation
 Probability density function
 Robustness
 Weighting function
 Industry Sectors
 Authors

 David Lee Duewer ^{(1)}
 Author Affiliations

 1. Analytical Chemistry Division, Stop 8390, Chemical Science and Technology Laboratory, National Institute of Standards and Technology, Gaithersburg, MD, 208998390, USA