Robust regression and outlier detection
Robust regression and outlier detection
Sensitivity analysis in linear regression
Sensitivity analysis in linear regression
A further comparison of tests of hypotheses in LAV regression
Computational Statistics & Data Analysis - Special issue on optimization techniques in statistics
A comparison of some quick algorithms for robust regression
Computational Statistics & Data Analysis
A bootstrap approach to hypothesis testing in least absolute value regression
Computational Statistics & Data Analysis
A note on hypothesis testing in LAV multiple regression: a small sample comparison
Computational Statistics & Data Analysis
BACON: blocked adaptive computationally efficient outlier nominators
Computational Statistics & Data Analysis
The Finite Sample Breakdown Point of \boldmath$\ell_1$-Regression
SIAM Journal on Optimization
Modern Applied Statistics with S
Modern Applied Statistics with S
The least trimmed quantile regression
Computational Statistics & Data Analysis
Weighted LAD-LASSO method for robust parameter estimation and variable selection in regression
Computational Statistics & Data Analysis
On simultaneously identifying outliers and heteroscedasticity without specific form
Computational Statistics & Data Analysis
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The least squares linear regression estimator is well-known to be highly sensitive to unusual observations in the data, and as a result many more robust estimators have been proposed as alternatives. One of the earliest proposals was least-sum of absolute deviations (LAD) regression, where the regression coefficients are estimated through minimization of the sum of the absolute values of the residuals. LAD regression has been largely ignored as a robust alternative to least squares, since it can be strongly affected by a single observation (that is, it has a breakdown point of 1/n, where n is the sample size). In this paper we show that judicious choice of weights can result in a weighted LAD estimator with much higher breakdown point. We discuss the properties of the weighted LAD estimator, and show via simulation that its performance is competitive with that of high breakdown regression estimators, particularly in the presence of outliers located at leverage points. We also apply the estimator to several data sets. ets.