Quantile Approximation for Robust Statistical Estimation and k-Enclosing Problems (2000)
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| Citations: | 5 - 1 self |
BibTeX
@MISC{Mount00quantileapproximation,
author = {David M. Mount and Nathan S. Netanyahu and Christine D. Piatko and Ruth Silverman and Angela Y. Wu},
title = {Quantile Approximation for Robust Statistical Estimation and k-Enclosing Problems},
year = {2000}
}
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Abstract
is concerned with finding the smallest shape of some type that encloses all the points of P . Well-known instances of this problem include finding the smallest enclosing box, minimum volume ball, and minimum volume annulus. In this paper we consider the following variant: Given a set of n points in R , find the smallest shape in question that contains at least k points or a certain quantile of the data. This type of problem is known as a k-enclosing problem. We present a simple algorithmic framework for computing quantile approximations for the minimum strip, ellipsoid, and annulus containing a given quantile of the points. The algorithms run in O(n log n) time.
