| Abstract: | Abstract. For the problem of estimating a sparse sequence of coefficients of a parametric or non-parametric generalized linear model, posterior mode estimation with a Subbotin( λ , ν ) prior achieves thresholding and therefore model selection when ν ∈ [0,1] for a class of likelihood functions. The proposed estimator also offers a continuum between the (forward/backward) best subset estimator ( ν = 0 ), its approximate convexification called lasso ( ν = 1 ) and ridge regression ( ν = 2 ). Rather than fixing ν , selecting the two hyperparameters λ and ν adds flexibility for a better fit, provided both are well selected from the data. Considering first the canonical Gaussian model, we generalize the Stein unbiased risk estimate, SURE( λ , ν ), to the situation where the thresholding function is not almost differentiable (i.e. ν 1 ). We then propose a more general selection of λ and ν by deriving an information criterion that can be employed for instance for the lasso or wavelet smoothing. We investigate some asymptotic properties in parametric and non-parametric settings. Simulations and applications to real data show excellent performance. |
