Quantile approximation for robust statistical estimation and k-enclosing problems

David M. Mount; Nathan S. Netanyahu; Christine D. Piatko; Ruth Silverman; Angela Y. Wu

doi:10.1142/S0218195900000334

Quantile approximation for robust statistical estimation and k-enclosing problems

David M. Mount, Nathan S. Netanyahu, Christine D. Piatko, Ruth Silverman, Angela Y. Wu

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

Abstract

Given a set P of n points in R^d, a fundamental problem in computational geometry 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^d, 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.

Original language	English
Pages (from-to)	593-608
Number of pages	16
Journal	International Journal of Computational Geometry and Applications
Volume	10
Issue number	6
DOIs	https://doi.org/10.1142/S0218195900000334
State	Published - Dec 2000

Keywords

LMS regression
Minimum enclosing disk
Minimum volume ball/ellipsoid/annulus estimator
Robust estimation

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10.1142/S0218195900000334

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AU - Mount, David M.

AU - Netanyahu, Nathan S.

AU - Piatko, Christine D.

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AU - Wu, Angela Y.

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Quantile approximation for robust statistical estimation and k-enclosing problems

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Keywords

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