Open Access
Translator Disclaimer
May, 1973 The Asymptotic Distribution of the Trimmed Mean
Stephen M. Stigler
Ann. Statist. 1(3): 472-477 (May, 1973). DOI: 10.1214/aos/1176342412


In this paper it is shown that in order for the trimmed mean to be asymptotically normal, it is necessary and sufficient that the sample be trimmed at sample percentiles such that the corresponding population percentiles are uniquely defined. (The sufficiency of this condition is well known.) In addition, the (non-normal) limiting distribution of the trimmed mean when this condition is not satisfied is derived, and it is shown that in some situations the use of the trimmed mean may lead to severely biased inferences. Some possible remedies are briefly discussed, including the use of "smoothly" trimmed means.


Download Citation

Stephen M. Stigler. "The Asymptotic Distribution of the Trimmed Mean." Ann. Statist. 1 (3) 472 - 477, May, 1973.


Published: May, 1973
First available in Project Euclid: 12 April 2007

zbMATH: 0261.62016
MathSciNet: MR359134
Digital Object Identifier: 10.1214/aos/1176342412

Rights: Copyright © 1973 Institute of Mathematical Statistics


Vol.1 • No. 3 • May, 1973
Back to Top