Least median of squares regression. (English) Zbl 0547.62046

Rousseeuw, Peter J.

J. Am. Stat. Assoc. 79, 871-880 (1984).

Summary: 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.

MSC:

62J05	Linear regression; mixed models
62F35	Robustness and adaptive procedures (parametric inference)

Keywords:

outliers; robust regression; breakdown point; least squares regression; median of the squared residuals; contamination