Computing Multivariate L1 Regression Estimates,
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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1992
- Accession Number
- ADP007121
Entities
People
- George R. Terrell
Organizations
- Virginia Tech