On the least median square problem

We consider the exact and approximate computational complexity of the multivariate LMS linear regression estimator. The LMS estimator is among the most widely used robust linear statistical estimators. Given a set of n points in IRd and a parameter k, the problem is equivalent to computing the slab bounded by two parallel hyperplanes of minimum separation that contains k of the points. We present algorithms for the exact and approximate versions of the multivariate LMS problem. We also provide nearly matching lower bounds on the computational complexity of these problems. The lower bounds hold if deciding whether d + 1 points are coplanar requires Ω(nd) time.

• Type: Conference
• Year: 2004
• Where: COMPGEOM
• Authors: Jeff Erickson, Sariel Har-Peled, David M. Mount
• Keywords: COMPGEOM 2004, Computational Complexity, LMS Linear Regression, Multivariate Lms