Accession Number : ADP007121

Title :   Computing Multivariate L1 Regression Estimates,

Corporate Author : VIRGINIA POLYTECHNIC INST AND STATE UNIV BLACKSBURG DEPT OF STATISTICS

Personal Author(s) : Terrell, George R.

Report Date : 1992

Pagination or Media Count : 4

Abstract : Minimum total error, or L1, regression estimates are a generalization of the sample median to prediction problems. Multivariate extensions therefore involve the concept of a multivariate median. There are many inequivalent characterizations of a multivariate median in the literature, all of which seem to have at least one of two major difficulties: either they lack the property of affine covariance which we have come to expect from ordinary multivariate regression, or they are computationally highly unpleasant. We here propose a definition of multivariate median, inspired by the theory of M-estimation, that transforms appropriately under linear changes of variables. Furthermore, it may be computed straightforwardly using a fixed-point property. The result is a resistant multivariate regression estimate that is intuitively appealing and, surprisingly, increasingly efficient at the normal model in higher dimensions. We share some computational experience with this estimator.

Descriptors :   *COVARIANCE, *REGRESSION ANALYSIS, *MULTIVARIATE ANALYSIS, ERRORS, ESTIMATES, MODELS, PREDICTIONS, THEORY, VARIABLES.

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE