Another look at the Grubbs estimators


Lombard, F.
Potgieter, C.J.

KAUST Grant Number


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.

Lombard F, Potgieter CJ (2012) Another look at the Grubbs estimators. Chemometrics and Intelligent Laboratory Systems 110: 74–80. Available:

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.

Elsevier BV

Chemometrics and Intelligent Laboratory Systems


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