Quantile approximation for robust statistical estimation

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.

• Type: Conference
• Year: 1998
• Where: CCCG
• Authors: David M. Mount, Nathan S. Netanyahu, Christine D. Piatko, Ruth Silverman, Angela Y. Wu
• Keywords: CCCG 1998, CCCG 2007, Minimum Volume, Minimum Volume Annulus, Smallest Shape