Meandian : A Measure of Location Based on Signed Rank of Deviations

A measure of location is examined that places itself where the signed rank deviations are as close to zero as possible. A solution algorithm is sketched. The measure is robust to outliers. In three illustrative real data examples we find the measure is usually intermediate between mean and median, hence provisionally called meandian. It tracks the mean and median closely when there is little skew. It is closer to the mean when skewing is light, but closer to the median when skewing is heavy. The measure has good stability when assessed using bootstrap resampling. Its connections with Wilcoxon’s signed rank test and the Hodges-Lehmann estimator are pointed out. The meandian may be generalized in a variety of ways, and breakdown points for the simple and generalized meandians are tabulated