Asymptotics for multivariate trimming

D. Nolan

Stochastic Processes and their Applications, 1992, vol. 42, issue 1, 157-169

Abstract: 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.

Keywords: robust; estimation; random; set; empirical; process; weak; convergence; cube-root; rate; of; convergence (search for similar items in EconPapers)
Date: 1992
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Citations: View citations in EconPapers (16)

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