Estimation of the error probability density from replicate measurements on several items

Abstract

Estimation of the measurement error probability density from data that consist of a few measurements on each of several dissimilar items is investigated. An estimator is proposed for independent and identically distributed measurement error with a symmetric density function. This estimator is based on an orthogonal function expansion. Computation begins with the differences between measurements on the same item and makes use of the fact that the characteristic function of these differences equals the square of the characteristic function of the measurement error. Application to robust inference for items measured in triplicate is considered. The M -estimates of the values of the items are compared on the basis of an estimated standard error computed from the density estimate. The circumstances under which this standard error estimator provides nearly valid inferences are delimited by Monte Carlo experiments.