Abstract
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.
Keywords
MathematicsStatisticsEstimatorSimple linear regressionTotal least squaresMultivariate statisticsRegressionLinear regressionBayesian multivariate linear regressionMean squared errorRobust regressionGeneralized least squaresLeast-squares function approximationRegression analysis
Affiliated Institutions
Related Publications
Partial least squares regression and projection on latent structure regression (PLS Regression)
Abstract Partial least squares (PLS) regression ( a.k.a. projection on latent structures) is a recent technique that combines features from and generalizes principal component a...
A Linear Spatial Correlation Model, with Applications to Positron Emission Tomography
Abstract A simple spatial-correlation model is presented for repeated measures data. Correlation between observations on the same subject is assumed to decay as a linear functio...
A Comparison of Least Squares and Latent Root Regression Estimators
Miilticollinesrity among the columns of regressor variables is known to cause severe distortion of the least squares estimates of the parameters in a multiple linear regression ...
Centroids
Abstract The concept of centroid is the multivariate equivalent of the mean. Just like the mean, the centroid of a cloud of points minimizes the sum of the squared distances fro...
Regression Shrinkage and Selection Via the Lasso
SUMMARY We propose a new method for estimation in linear models. The ‘lasso’ minimizes the residual sum of squares subject to the sum of the absolute value of the coefficients b...
Publication Info
- Year
- 1984
- Type
- article
- Volume
- 79
- Issue
- 388
- Pages
- 871-880
- Citations
- 3497
- Access
- Closed
External Links
Social Impact
Altmetric
PlumX Metrics
Social media, news, blog, policy document mentions
Citation Metrics
3497
OpenAlex
Cite This
Peter J. Rousseeuw
(1984).
Least Median of Squares Regression.
Journal of the American Statistical Association
, 79
(388)
, 871-880.
https://doi.org/10.1080/01621459.1984.10477105
Identifiers
- DOI
- 10.1080/01621459.1984.10477105