Lasso, knockoff and Gaussian covariates: a comparison
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Given data y and k covariates x_j one problem in linear regression is to decide which if any of the covariates to include when regressing the dependent variable y on the covariates x_j. In this paper three such methods, lasso, knockoff and Gaussian covariates are compared using simulations and real data. The Gaussian covariate method is based on exact probabilities which are valid for all y and x_j making it model free. Moreover the probabilities agree with those based on the F-distribution for the standard linear model with i.i.d. Gaussian errors. It is conceptually, mathematically and algorithmically very simple, it is very fast and makes no use of simulations. It outperforms lasso and knockoff in all respects by a considerable margin.
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