Least median squares regression

Multivariate models using neural networks, support vector machines and least median squares regression have been used to predict hERG activity [96-98]. These types of models function more as computational black box assays. 

Least Median Squares regression N = 1075 patch clamping IC50 data. N = 1679 IC50 and single point data. Test set R2 = 0.54 RMSE = 0.63 Volsurf and other descriptors. 178... 

Firstly, the krlglng estimator is optimal only for the least square criterion. Other criteria are known which yield no more complicated estimators such as the minimization of the mean absolute deviation (mAD), E P(2c)-P (3c), yielding median-type regression estimates. 

Rousseeuw, P. J. J. Amer. Stat. Assoc. 79, 1984, 871-880. Least median of squares regression. 

Some methods, therefore, take as the best pair of regression coefficients that which gives the least median of squares ... 

For multiple regression, the least median of squares (LMS) of Rousseeuw [7] and the LTS described previously were the first equivariant methods to attain a 50% breakdown value. Their low finite-sample efficiency can be improved by carrying out a one-step reweighed least-squares fit (Equation 6.9) afterward. Another approach is to compute a one-step M-estimator starting from LMS or LTS, which also maintains the breakdown value and yields the same efficiency as the corresponding M-estimator. In order to combine these advantages with those of the bounded-influence approach, it was later proposed to follow the LMS or LTS by a one-step GM-estimator [35],... 

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