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Least Median of Squares Regression
Peter J. Rousseeuw
Journal of the American Statistical Association
Vol. 79, No. 388 (Dec., 1984), pp. 871-880
Stable URL: http://www.jstor.org/stable/2288718
Page Count: 10
You can always find the topics here!Topics: Estimators, Point estimators, Statistical estimation, Statistics, Least squares, Hyperplanes, Linear regression, Statistical median, Objective functions, Linear models
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Classical least squares regression consists of minimizing the sum of the squared residuals. Many authors have produced more robust versions of this estimator by replacing the square by something else, such as the absolute value. In this article a different approach is introduced in which the sum is replaced by the median of the squared residuals. The resulting estimator can resist the effect of nearly 50% of contamination in the data. In the special case of simple regression, it corresponds to finding the narrowest strip covering half of the observations. Generalizations are possible to multivariate location, orthogonal regression, and hypothesis testing in linear models.
Journal of the American Statistical Association © 1984 American Statistical Association