Estimation of a mean in the presence of an extreme observation

The performance of Anscombe, semi-Winsorization and Winsorization (A, S and W) rules for dealing with extreme observations are investigated for observations from N(μ, σ²) and the simple case where it is assumed that at most one observation in the sample may be biased, arising from N(μ + aσ, σ²) and the primary objective is to estimate μ when σ is unknown. Each of these rules is separately treated in terms of the estimated standard deviation, range and interquartile range. A Monte Carlo method is used to evaluate certain expectation integrals that arise in the computations. We give the results for sample sizes n = 6, 8, 10, 12, 14, 16, 20, 30, 40, 50, 60, 80, 100 of determining the constants necessary to give ‘premiums’ of 0.01 and 0.05 for each of the rules. The performance of the rules is measured in terms of ‘protection’. Features of the resulting tables are discussed.