# Least Median of Squares Regression

CiteWeb id: 20120000077

CiteWeb score: 3144

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.

**Least Median of Squares Regression**" is placed in the Top 10000 of the best publications in CiteWeb. Also in the category Mathematics it is included to the Top 1000. Additionally, the publicaiton "

**Least Median of Squares Regression**" is placed in the Top 100 among other scientific works published in 2012.

- web.ipac.caltech.edu/staff/fmasci/home/astro_refs/LeastMedianOfSquares.pdf
- www.tandfonline.com/doi/pdf/10.1080/01621459.1984.10477105
- www.jstor.org/stable/2288718?origin=crossref
- spider.ipac.caltech.edu/staff/fmasci/home/statistics_refs/LeastMedianOfSquares.pdf
- www.eecs.yorku.ca/course_archive/2010-11/W/6338/lectures/LeastMedianOfSquares.pdf
- amstat.tandfonline.com/doi/pdf/10.1080/01621459.1984.10477105
- www.tandfonline.com/doi/abs/10.1080/01621459.1984.10477105
- ci.nii.ac.jp/naid/30022469649
- dx.doi.org/10.1080/01621459.1984.10477105

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