Estimation of a Mean When One Observation May Be Spurious

Two procedures for estimating the mean of a normal distribution when one of the observations may be spurious are presented. Given a sample of size n assumed to have been obtained from a normal population with mean μ and known variance σ2 it is possible that one of the observed values is distributed as N(μ + bσ, σ2). A weighted estimator for μ is proposed, and a weighing function based on the largest absolute deviation from the sample mean is obtained, A modification of the weighted estimator is also considered. The mean square errors of both estimation procedures are obtained for samples of size 3 and are used as a basis for evaluating their performances. The performances of the estimators relative to the sample mean, and to other estimators that have been proposed, are presented.