Handle URI:
http://hdl.handle.net/10754/597584
Title:
Another look at the Grubbs estimators
Authors:
Lombard, F.; Potgieter, C.J.
Abstract:
We consider estimation of the precision of a measuring instrument without the benefit of replicate observations on heterogeneous sampling units. Grubbs (1948) proposed an estimator which involves the use of a second measuring instrument, resulting in a pair of observations on each sampling unit. Since the precisions of the two measuring instruments are generally different, these observations cannot be treated as replicates. Very large sample sizes are often required if the standard error of the estimate is to be within reasonable bounds and if negative precision estimates are to be avoided. We show that the two instrument Grubbs estimator can be improved considerably if fairly reliable preliminary information regarding the ratio of sampling unit variance to instrument variance is available. Our results are presented in the context of the evaluation of on-line analyzers. A data set from an analyzer evaluation is used to illustrate the methodology. © 2011 Elsevier B.V.
Citation:
Lombard F, Potgieter CJ (2012) Another look at the Grubbs estimators. Chemometrics and Intelligent Laboratory Systems 110: 74–80. Available: http://dx.doi.org/10.1016/j.chemolab.2011.09.013.
Publisher:
Elsevier BV
Journal:
Chemometrics and Intelligent Laboratory Systems
KAUST Grant Number:
KUS-C1-016-04
Issue Date:
Jan-2012
DOI:
10.1016/j.chemolab.2011.09.013
Type:
Article
ISSN:
0169-7439
Sponsors:
The first author's work was supported by the National Research Foundation of South Africa. The second author's work was supported by Award No. KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST). The authors thank two referees for valuable comments that led to the correction of some errors and to an improved exposition of the work.
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Full metadata record

DC FieldValue Language
dc.contributor.authorLombard, F.en
dc.contributor.authorPotgieter, C.J.en
dc.date.accessioned2016-02-25T12:42:32Zen
dc.date.available2016-02-25T12:42:32Zen
dc.date.issued2012-01en
dc.identifier.citationLombard F, Potgieter CJ (2012) Another look at the Grubbs estimators. Chemometrics and Intelligent Laboratory Systems 110: 74–80. Available: http://dx.doi.org/10.1016/j.chemolab.2011.09.013.en
dc.identifier.issn0169-7439en
dc.identifier.doi10.1016/j.chemolab.2011.09.013en
dc.identifier.urihttp://hdl.handle.net/10754/597584en
dc.description.abstractWe consider estimation of the precision of a measuring instrument without the benefit of replicate observations on heterogeneous sampling units. Grubbs (1948) proposed an estimator which involves the use of a second measuring instrument, resulting in a pair of observations on each sampling unit. Since the precisions of the two measuring instruments are generally different, these observations cannot be treated as replicates. Very large sample sizes are often required if the standard error of the estimate is to be within reasonable bounds and if negative precision estimates are to be avoided. We show that the two instrument Grubbs estimator can be improved considerably if fairly reliable preliminary information regarding the ratio of sampling unit variance to instrument variance is available. Our results are presented in the context of the evaluation of on-line analyzers. A data set from an analyzer evaluation is used to illustrate the methodology. © 2011 Elsevier B.V.en
dc.description.sponsorshipThe first author's work was supported by the National Research Foundation of South Africa. The second author's work was supported by Award No. KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST). The authors thank two referees for valuable comments that led to the correction of some errors and to an improved exposition of the work.en
dc.publisherElsevier BVen
dc.subjectGrubbs' estimatorsen
dc.subjectInstrument precisionen
dc.subjectOnline analyzersen
dc.titleAnother look at the Grubbs estimatorsen
dc.typeArticleen
dc.identifier.journalChemometrics and Intelligent Laboratory Systemsen
dc.contributor.institutionNorth-West University, Potchefstroom, South Africaen
dc.contributor.institutionUniversity of Johannesburg, Johannesburg, South Africaen
dc.contributor.institutionTexas A and M University, College Station, United Statesen
kaust.grant.numberKUS-C1-016-04en
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