On Searls’ winsorized mean for skewed populations - ARCHIVED

This paper considers the winsorized mean as an estimator of the mean of a positive skewed population. A winsorized mean is obtained by replacing all the observations larger than some cut-off value R by R before averaging. The optimal cut-off value, as defined by Searls (1966), minimizes the mean square error of the winsorized estimator. Techniques are proposed for the evaluation of this optimal cut-off in several sampling designs including simple random sampling, stratified sampling and sampling with probability proportional to size. For most skewed distributions, the optimal winsorization strategy is shown, on average, to modify the value of about one data point in the sample. Closed form approximations to the efficiency of Searls’ winsorized mean are derived using the theory of extreme order statistics. Various estimators reducing the impact of large data values are compared in a Monte Carlo experiment.