Smooth Blockwise Iterative Thresholding: A Smooth Fixed Point Estimator Based on the Likelihood's Block Gradient

• 成果类型: Article
• 署名作者: Sardy, Sylvain
• 署名单位: University of Geneva
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2012.664527
• 发表日期: 2012
• 页码: 800-813
• 关键词: VARIABLE SELECTION; wavelet; regression; regularization; algorithm; sparsity

摘要

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 lambda and nu, and a smoothness parameter s. 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 lambda and nu, 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 s tempers the erraticity of the risk estimate, and derives a universal threshold, an information criterion, and an oracle inequality in this canonical setting.