Computing the least median of squares estimator in time O(nd)

Authors:
Thorsten Bernholt
Affiliations:
Lehrstuhl Informatik 2, Universität Dortmund, Germany
Venue:
ICCSA'05 Proceedings of the 2005 international conference on Computational Science and its Applications - Volume Part I
Year:
2005

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Abstract

In modern statistics, the robust estimation of parameters of a regression hyperplane is a central problem, i. e., an estimation that is not or only slightly affected by outliers in the data. In this paper we will consider the least median of squares (LMS) estimator. For n points in d dimensions we describe a randomized algorithm for LMS running in O(nd) time and O(n) space, for d fixed, and in time O(d3 (2n)d) and O(dn) space, for arbitrary d.