Asymptotic efficiency of the Spearman estimator and characterizations of distributions (Q1093276)

The Spearman estimator is designed to be a nonparametric estimator for the expectation of a tolerance distribution. We characterize the one- parameter families of distributions (the parameter being the mean of the distribution) for which the Spearman estimator has asymptotic efficiency one. In particular, when the parameter indexes the location, the characterizing distribution is the logistic distribution. In any other case of efficiency one, the family of distributions is given by certain transformations of a logistic distribution.