The Asymptotic Distribution of the Trimmed Mean.

Abstract

In the 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. (Author)

Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1972
Accession Number
AD0747324

Entities

People

  • Stephen M. Stigler

Organizations

  • University of Wisconsin–Madison

Tags

Fields of Study

  • Mathematics

Readers

  • Statistical inference.
  • Systems Analysis and Design

Technology Areas

  • AI & ML
  • AI & ML - Bayesian Inference
  • AI & ML - Machine Learning Algorithms