LQD: RATS module for regression via least quartile difference estimator
lqd.src computes a robust linear regression called the least quartile difference estimator (lqd). it was proposed in Christophe Croux, Peter J. Rousseeuw, and Ola Hossjer (1994), "Generalized s-estimators," Journal of the American Statistical Association, 89, 1271-1281. The lqd is closely related to other high-breakdown, computer-intensive regression methods like least median of squares and least trimmed squares. All these methods are very effective at detecting outliers and leverage points in data. When the random errors are in fact uncontaminated Gaussian variables, lqd is more efficient than these other high-breakdown methods. (its asymptotic efficiency is about 67 percent compared to least squares at a Gaussian distribution; the asymptotic efficiency of lms is zero and that of lts is just 8 percent.) Moreover, the lqd regression coefficients are asymptotically Gaussian with a covariance matrix proportional to the inverse of X'X.
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