# A Review of Some Asymptotic Properties of Trimmed Sums of Multivariate Data

• R. A. Maller
Part of the Progress in Probability book series (PRPR, volume 23)

## Abstract

‘Trimming’ in this article will be used to describe the idea of removing points of a sample (usually ‘extreme points’) in order to improve the properties of estimators based on the sample. We will also consider procedures in which sample points are weighted so that the influence of the extremes is reduced. The sample will always consist of n independent and identically distributed (iid) random vectors in ℝd, and our emphasis will be on the (asymptotic) behaviour of that portion of it which remains after deleting or downweighting the extremes, rather than in the behaviour of the extremes themselves. The object of interest will be the estimation of location or scale of the distribution of the Sample, or more precisely, in the ‘robust’ estimation of location and scale due to removal or downweighting of extremes. Thus we are led to the investigation of the asymptotic properties of ‘trimmed sums’ (or ‘trimmed means’ or ‘robust variance matrices’) in ℝd.

## Keywords

Convex Hull Order Statistic Asymptotic Normality Iterate Logarithm Minimum Covering

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