Accession Number:

ADP007121

Title:

Computing Multivariate L1 Regression Estimates,

Descriptive Note:

Corporate Author:

VIRGINIA POLYTECHNIC INST AND STATE UNIV BLACKSBURG DEPT OF STATISTICS

Personal Author(s):

• Terrell, George R.

Report Date:

1992-01-01

Pagination or Media Count:

4.0

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