Smooth James-Stein model selection against erratic Stein unbiased risk estimate to select several regularization parameters

Smooth James-Stein thresholding-based estimators enjoy smoothness like ridge regression and perform variable selection like lasso. They have added flexibility thanks to more than one regularization parameters (like adaptive lasso), and the ability to select these parameters well thanks to a unbiased and smooth estimation of the risk. The motivation is a gravitational wave burst detection problem from several concomitant high-frequency time series. A wavelet-based esti-mator is developed to combine information from all captors by block-thresholding multiresolution coefficients. We derive a universal threshold , an information criterion and an oracle inequality for this estimator. Smooth James-Stein thresholding is then employed in parametric linear regression for which we derive a formula for unbiased risk estimation. 1 Smooth James Stein 2 We perform a Monte-Carlo simulation to quantify the improvement and investigate the oracle property of smooth adaptive lasso empirically. Introducing the smoothness parameter allows smooth versions of existing estimators, for which we derive their equivalent degrees of freedom. Conversely, letting the smoothness parameter tend to one, we derive the equivalent degrees of freedom of lasso, adaptive lasso and group lasso. So far, only that of lasso is known.