Symmetric quantile averages and related estimators

The average of two complementary order statistics is termed a symmetric quantile average. In addition to having quite good efficiency, robustness and computational properties, exact nonparametric confidence intervals for location can be derived from it. A related type of estimator called a combined quantile average is introduced; it is slightly more difficult to compute than the symmetric quantile average, but can have better efficiency and robustness properties. In fact the recommended form of combined quantile average is comparable for robustness and normal efficiency with the 15% trimmed mean, but in addition it leads, like symmetric quantile averages, to the definition of exact nonparametric confidence intervals.