Summary
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.
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The author's research is supported by a Grant from the Office of Naval Research, Grant No. N00014-84-K-0184. Reproduction in whole or in part is permitted for any purpose of the U.S. Government.
The author's research is supported by the Royal Norwegian Council for Scientific and Industrial Research.
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Govindarajulu, Z., Lindqvist, B.H. Asymptotic efficiency of the Spearman estimator and characterizations of distributions. Ann Inst Stat Math 39, 349–361 (1987). https://doi.org/10.1007/BF02491473
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DOI: https://doi.org/10.1007/BF02491473