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Title: Solution path based variable selection Authors:  Karl Gregory - University of South Carolina (United States) [presenting]
Abstract: Methods are considered for variable selection in high-dimensional regression based on the solution paths of sparse estimators. In particular, we measure the importance of a covariate by the amount of sparsity penalization it is able to overcome in order to enter the model, for example under LASSO penalization or along the path of the least angle regression algorithm. In addition, we consider measuring the importance of a covariate by how much the solution path of a sparsity-promoting estimator changes when the covariate is removed from the model. We study the performance of variable screening procedures based on these metrics as well as the performance of bootstrap methods for estimating their distributions under certain null hypotheses in the regression coefficients.