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Biometrika 1982 69(1):55-59; doi:10.1093/biomet/69.1.55
© 1982 by Biometrika Trust
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Representations of the space of distributions useful in robust estimation of location

DAVID L. HALL and BRIAN L. JOINER

Statistics Section, Battelle Pacific Northwest Laboratories Richland, Washington, USA
Department of Statistics, University of Wisconsin Madison, Wisconsin, USA

In many situations it is useful to have a low-dimensional representation of the space of distributions. This paper gives one-, two- and three-dimensional representations which are particularly relevant to the study of robust estimation of location based on rank estimators. The distances are defined as functions of the asymptotic relative efficiency of the most efficient rank estimator for one distribution when used on data from another distribution. Values of these distance functions are computed for a large number of pairs of distributions and multidimensional scaling is used to find the low-dimensional representations.

Key Words: Adaptive estimation • Asymptotic relative efficiency • Contaminated normal distribution • Lambda distribution • Multidimensional scaling • Rank estimator • t distribution


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