Abstract We consider the problem of building a linear prediction model when the number of candidate covariates is large and the dataset contains a fraction of outliers and other contaminations that are difficult to visualize and clean. We aim at predicting the future non-outlying cases. Therefore, we need methods that are robust and scalable at the same time.

Our two-step model building procedure consists of sequencing and segmentation. In sequencing, we order the covariates and the first m covariates form a reduced set for further consideration. The segmentation step carefully examines subsets of the covariates in the reduced set to select the final prediction model.

We need a suitable step–by–step algorithm to sequence the covariates. Since Forward Selection (FS) is aggressive, we focus on Least Angle Regression (LARS), a powerful algorithm recently proposed by Efron, Hastie, Johnstone and Tibshirani (2004). We review LARS, and explain one approach to its robustification.