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The proposed smooth blockwise iterative thresholding estimator (SBITE) is amodel selection technique defined as a fixed point reached by iterating alikelihood gradient-based thresholding function. The smooth James-Steinthresholding function has two regularization parameters $\lambda$ and $\nu$,and a smoothness parameter $s$. It enjoys smoothness like ridge regression andselects variables like lasso. Focusing on Gaussian regression, we show thatSBITE is uniquely defined, and that its Stein unbiased risk estimate is asmooth function of $\lambda$ and $\nu$, for better selection of the tworegularization parameters. We perform a Monte-Carlo simulation to investigatethe predictive and oracle properties of this smooth version of adaptive lasso.  The motivation is a gravitational wave burst detection problem from severalconcomitant time series. A nonparametric wavelet-based estimator is developedto combine information from all captors by block-thresholding multiresolutioncoefficients. We study how the smoothness parameter $s$ tempers the erraticityof the risk estimate, and derive a universal threshold, an informationcriterion and an oracle inequality in this canonical setting.

Smooth blockwise iterative thresholding: a smooth fixed point estimator based on the likelihood's block gradient