A Linear Parameter Estimator

by Deborah Sturm.

Abstract: A method is presented for determining the parameters of linear model functions which performs well in the presence of outliers. Like the M-estimator method, our method, inner products (IP) is a generalization of Least Squares (LS) and yilds robust results. Unlike M-estimators, IP always leads to linear equations which are easy to solve. The IP method consists of multiplying the residuals by weighted coefficients, and then solving the summed equations for the unknown parameters. The weights, which are functions of the data, are chosen so that the influence of outliers is reduced. Results of computer experiments are presented which show IP to be as robust as but computationally simpler than the classical M-estimator methods.

Key Words: Robust Linear Regression, outliers

Deborah Sturm, sturm@mail.csi.cuny.edu

Editor: Jeff Simonoff,jsimonof@stern.nyu.edu

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