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Abstract:
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A number of variable selection methods have been proposed involving nonconvex penalty functions. These methods, which include the bridge, SCAD, and MCP penalties, have been demonstrated to have attractive theoretical properties, but optimization of their objective functions is not a straightforward task. Here, we demonstrate the potential of coordinate descent algorithms for fitting these models. We establish theoretical convergence properties of the algorithms as well as investigate their efficiency using simulation studies. We find that coordinate descent algorithms are significantly faster than competing approaches, particularly for high-dimensional problems.
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