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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
DOI: 10.2307/2288718
Stable URL: http://www.jstor.org/stable/2288718
Page Count: 10
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Least Median of Squares Regression
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Abstract

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.

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