Asymptotics for multivariate trimming
One version of multivariate trimming is the operation that intersects all halfspaces with probability content 1-[alpha] or greater. The result is a [alpha]-trimmed convex set, and this set is stochastic when the empirical distribution of a sample determines the probability content of the halfspaces. In this paper, conditions are found for the weak convergence of the boundary of this set to a Gaussian process. It is also shown that an n1/3 normalization produces a limit distribution for the direction normal to the boundary of the set. Intuitive geometric arguments and empirical process methods are employed to establish both limit results.
Year of publication: |
1992
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Authors: | Nolan, D. |
Published in: |
Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 42.1992, 1, p. 157-169
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Publisher: |
Elsevier |
Keywords: | robust estimation random set empirical process weak convergence cube-root rate of convergence |
Saved in:
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