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 smoothn...

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Vydáno v:	Journal of the American Statistical Association Ročník 107; číslo 498; s. 800 - 813
Hlavní autor:	Sardy, Sylvain
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Alexandria Taylor & Francis Group 01.06.2012 Taylor & Francis Ltd
Témata:	Adaptive lasso Analytical estimating Bias Estimation Estimation methods Estimators Function Grammatical aspect Gravitational waves Inequality Information criterion Iterative block thresholding James-Stein estimator Mathematical independent variables Modeling Monte Carlo method Monte Carlo methods Monte Carlo simulation Motivation Multivariate analysis Multivariate time series Oracles Property Regression analysis Risk risk estimate Simulation Sparse model selection Statistics Theory and Methods Threshing Time series time series analysis Time series models Unbiased estimators Universal threshold Wavelet smoothing
ISSN:	1537-274X, 0162-1459, 1537-274X
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Popis
Shrnutí:	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 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 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 s tempers the erraticity of the risk estimate, and derives a universal threshold, an information criterion, and an oracle inequality in this canonical setting.
Bibliografie:	http://dx.doi.org/10.1080/01621459.2012.664527 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14 ObjectType-Article-2 content type line 23 ObjectType-Article-1 ObjectType-Feature-2
ISSN:	1537-274X 0162-1459 1537-274X
DOI:	10.1080/01621459.2012.664527