Efficient Methods for Estimating the Mean Using an Adaptive Scheme Involving Two or Three Measurements

Janos Bottyan
Master’s Candidate, Department of Statistics
Colorado State University
Monday, 6 December 2004
9:00 AM
115 Natural Resources Building



Although replicate measurements are desirable in many routine measurement situations, economic and time considerations limit the number of possible replicates to two or three only. A not so uncommon practice in such cases is for the investigator to make two replicate measurements, but if these two measurement appear to not agree sufficiently well with each other, to take a third measurement. This is especially so in situations where outliers are expected. How the third measurement is handled is protocol dependent. One measurement protocol calls for omitting the most "discrepant" observation and using the mean of the remaining two measurements. Another protocol calls for using the average of all three measurements. In this paper we investigate the properties of estimators arising from different measurement protocols in a loss function framework where there is a cost associated with the third measurement, if it is made, and a penalty associated with the mean squared error of the estimator.



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