UBC Theses and Dissertations
Linear model selection based on extended robust least angle regression Zhang, Hongyang
In variable selection problems, when the number of candidate covariates is relatively large, the "two-step" model building strategy, which consists of two consecutive steps sequencing and segmentation, is often used. Sequencing aims to first sequence all the candidate covariates to form a list of candidate variables in which more "important" ones are likely to appear at the beginning. Then, in the segmentation step, the subsets of the first m (chosen by the user) candidate covariates which are ranked at the top of the sequenced list will be carefully examined in order to select the final prediction model. This thesis mainly focuses on the sequencing step. Least Angle Regression (LARS), proposed by Efron, Hastie, Johnstone and Tibshirani (2004), is a quite powerful step-by-step algorithm which can be used to sequence the candidate covariates in order of their importance. Khan, J.A., Van Aelst, S., and Zamar, R.H. (2007) further proposed its robust version --- Robust LARS. Robust LARS is robust against outliers and computationally efficiency. However, neither the original LARS nor the Robust LARS is available for carrying out the sequencing step when the candidate covariates contain both continuous and nominal variables. In order to remedy this, we propose the Extended Robust LARS by proposing the generalized definitions of correlations which includes the correlations between nominal variables and continuous variables. Simulations and real examples are used to show that the Extended Robust LARS gives superior performance to two of its competitors, the classical Forward Selection and Group Lasso.
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