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Robustness of Location Estimators Under Changes of Population Kurtosis

Ralph B. D'Agostino and Austin F. S. Lee
Journal of the American Statistical Association
Vol. 72, No. 358 (Jun., 1977), pp. 393-396
DOI: 10.2307/2286805
Stable URL: http://www.jstor.org/stable/2286805
Page Count: 4
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Robustness of Location Estimators Under Changes of Population Kurtosis
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Abstract

We investigate the robustness of various estimators of the mean for two families of symmetric distributions (exponential power and t) indexed by the kurtosis γ and Hogg's (1972) measure of tail thickness Q. For fixed γ or Q, the optimal estimator for one family is often inefficient for the other family. Furthermore, over various ranges of γ or Q some common estimators (e.g., the median) are efficient only for one family. However, other estimators (e.g., some trimmed means and Gastwirth's three-percentile estimator (1966)) do maintain good efficiency over a wide range of γ or Q.

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