Asymptotic Normality of U-Statistics Based on Trimmed Samples.
Abstract
For robust estimation of location, the ordinary sample mean is too sensitive to outliers. A classical and successful alternative is the trimmed mean, for which asymptotic normality was established by Bickel (1965). As discussed by Bickel and Lehmann (1975), for example, the trimmed mean remains relatively efficient with respect to the untrimmed mean even in the absence of outliers. Viewing the trimmed mean as simply the ordinary mean defined on a trimmed sample, we are motivated to consider other common statistics as well in this regard. This paper studies U-statistics in such fashion. The class of U-statistics, introduced by Hoeffding (1948), contains a wealth of statistics of interest in their own rights and also contains statistics which serve as approximations to statistics of more complicated type. A very significant broadening of the scope of robust statistical inference is achieved, therefore, by consideration of the class of U-statistics on trimmed samples.
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 01, 1985
- Accession Number
- ADA163346
Entities
People
- Noel Veraverbeke
- Paul M Janssen
- Robert Serfling
Organizations
- Johns Hopkins University