Smooth Blockwise Iterative Thresholding: A Smooth Fixed Point Estimator Based on the Likelihood’s Block Gradient
The proposed smooth blockwise iterative thresholding estimator (SBITE) is a model selection technique defined as a fixed point reached by iterating a likelihood gradient-based thresholding function. The smooth James--Stein thresholding function has two regularization parameters λ and ν, and a smoothness parameter <italic>s</italic>. It enjoys smoothness like ridge regression and selects variables like lasso. Focusing on Gaussian regression, we show that SBITE is uniquely defined, and that its Stein unbiased risk estimate is a smooth function of λ and ν, for better selection of the two regularization parameters. We perform a Monte Carlo simulation to investigate the predictive and oracle properties of this smooth version of adaptive lasso. The motivation is a gravitational wave burst detection problem from several concomitant time series. A nonparametric wavelet-based estimator is developed to combine information from all captors by block-thresholding multiresolution coefficients. We study how the smoothness parameter <italic>s</italic> tempers the erraticity of the risk estimate, and derives a universal threshold, an information criterion, and an oracle inequality in this canonical setting.
Year of publication: |
2012
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Authors: | Sardy, Sylvain |
Published in: |
Journal of the American Statistical Association. - Taylor & Francis Journals, ISSN 0162-1459. - Vol. 107.2012, 498, p. 800-813
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Publisher: |
Taylor & Francis Journals |
Saved in:
Saved in favorites
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