Usage Note 23195: Which SAS procedures produce Quantile, Median, Least Absolute Vaue, and Mean Absolute Value regressions?
Currently, we offer some routines in SAS/IML software to do regression quantiles and robust regression. The LAV (least absolute value estimation technique), LMS (least median of squares), LTS (least trimmed squares) and MVE (minimum volume ellipsoid estimation) subroutines are available and documented in the Version 8 SAS/IML OnlineDoc. It is possible we will have a procedures for various types of robust regression in a future release of SAS. The following is some information about the routines for outlier detection and robust regression. There is an example about regression quantiles in the SAS/IML User's Guide.
SAS/IML has three subroutines that can be used for outlier detection and robust regression. The Least Median of Squares (LMS) and Least Trimmed Squares (LTS) subroutines perform robust regression (sometimes called resistant regression). These subroutines are able to detect outliers and perform a least-squares regression on the remaining observations.
The Minimum Volume Ellipsoid Estimation (MVE) subroutine can be used to find the minimum volume ellipsoid estimator, which is the location and robust covariance matrix that can be used for constructing confidence regions and for detecting multivariate outliers and leverage points. Moreover, the MVE subroutine provides a table of robust distances and classical Mahalanobis distances. The LMS, LTS, and MVE subroutines and some other robust estimation theories and methods were developed by Rousseeuw (1984) and Rousseeuw and Leroy (1987). Some statistical applications for MVE are described in Rousseeuw and Van Zomeren (1990).
Rousseeuw, P.J. (1984), "Least Median of Squares Regression," Journal of the American Statistical Association, 79, 871 -880.
Rousseeuw, P.J. (1985), "Multivariate Estimation with High Breakdown Point," in Mathematical Statistics and Applications, Dordrecht: Reidel Publishing Company, 283 -297.
Rousseeuw, P.J. and Hubert, M. (1996), "Recent Developments in PROGRESS," Technical Report, University of Antwerp.
Rousseeuw, P.J. and Leroy, A.M. (1987), Robust Regression and Outlier Detection, New York: John Wiley & Sons, Inc.
Rousseeuw, P.J. and Van Zomeren, B.C. (1990), "Unmasking Multivariate Outliers and Leverage Points," Journal of the American Statistical Association, 85, 633 -639.
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