A Generalized Dantzig Selector with Shrinkage Tuning
نویسنده
چکیده
The Dantzig selector performs variable selection and model fitting in linear regression. It uses an L1 penalty to shrink the regression coefficients towards zero, in a similar fashion to the Lasso. While both the Lasso and Dantzig selector potentially do a good job of selecting the correct variables, they tend to over-shrink the final coefficients. This results in an unfortunate trade-off. One can either select a high shrinkage tuning parameter that produces an accurate model but poor coefficient estimates or a low shrinkage parameter that produces more accurate coefficients but includes many irrelevant variables. We extend the Dantzig selector to fit generalized linear models while also eliminating over-shrinkage of the coefficient estimates. In addition, we develop a computationally efficient algorithm, similar in nature to least angle regression, to compute the entire path of coefficient estimates. A detailed simulation study illustrates the advantages of our approach relative to several other possible methods. Finally, we apply the methodology to two real-world datasets.
منابع مشابه
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The Dantzig selector (Candes and Tao, 2007) is a new approach that has been proposed for performing variable selection and model fitting on linear regression models. It uses an L1 penalty to shrink the regression coefficients towards zero, in a similar fashion to the Lasso. While both the Lasso and Dantzig selector potentially do a good job of selecting the correct variables, several researcher...
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