TY - JOUR

T1 - Quantile approximation for robust statistical estimation and k-enclosing problems

AU - Mount, David M.

AU - Netanyahu, Nathan S.

AU - Piatko, Christine D.

AU - Silverman, Ruth

AU - Wu, Angela Y.

PY - 2000/12

Y1 - 2000/12

N2 - Given a set P of n points in Rd, 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 Rd, 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.

AB - Given a set P of n points in Rd, 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 Rd, 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.

KW - LMS regression

KW - Minimum enclosing disk

KW - Minimum volume ball/ellipsoid/annulus estimator

KW - Robust estimation

UR - http://www.scopus.com/inward/record.url?scp=0034555431&partnerID=8YFLogxK

U2 - 10.1142/S0218195900000334

DO - 10.1142/S0218195900000334

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AN - SCOPUS:0034555431

SN - 0218-1959

VL - 10

SP - 593

EP - 608

JO - International Journal of Computational Geometry and Applications

JF - International Journal of Computational Geometry and Applications

IS - 6

ER -