Tuning parameter selection in sparse regression modeling
In sparse regression modeling via regularization such as the lasso, it is important to select appropriate values of tuning parameters including regularization parameters. The choice of tuning parameters can be viewed as a model selection and evaluation problem. Mallows’ Cp type criteria may be used as a tuning parameter selection tool in lasso type regularization methods, for which the concept of degrees of freedom plays a key role. In the present paper, we propose an efficient algorithm that computes the degrees of freedom by extending the generalized path seeking algorithm. Our procedure allows us to construct model selection criteria for evaluating models estimated by regularization with a wide variety of convex and nonconvex penalties. The proposed methodology is investigated through the analysis of real data and Monte Carlo simulations. Numerical results show that Cp criterion based on our algorithm performs well in various situations.
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- Mazumder, Rahul & Friedman, Jerome H. & Hastie, Trevor, 2011. "SparseNet: Coordinate Descent With Nonconvex Penalties," Journal of the American Statistical Association, American Statistical Association, vol. 106(495), pages 1125-1138.
- Hui Zou & Trevor Hastie, 2005. "Addendum: Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 768-768.
- Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
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- Hui Zou & Trevor Hastie, 2005. "Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(2), pages 301-320.
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