Conditional variable screening via ordinary least squares projection
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To deal with the growing challenge from high dimensional data, we propose a conditional variable screening method for linear models named as conditional screening via ordinary least squares projection (COLP). COLP can take advantage of prior knowledge concerning certain active predictors by eliminating the adverse impacts from their coefficients in the estimation of remaining ones and thus significantly enhance the screening accuracy. We then prove the sure screening property of COLP under reasonable assumptions. Moreover, based on the conditional approach, we introduce an iterative algorithm named as forward screening via ordinary least squares projection (FOLP), which not only could utilize the prior knowledge more effectively, but also has promising performances when no prior information is available applying a data-driven conditioning set. The competence of COLP and FOLP is fully demonstrated in extensive numerical studies and the application to a leukemia dataset.
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