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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Bibliographic Details
Published in:Journal of the American Statistical Association Vol. 107; no. 498; pp. 800 - 813
Main Author: Sardy, Sylvain
Format: Journal Article
Language:English
Published: Alexandria Taylor & Francis Group 01.06.2012
Taylor & Francis Ltd
Subjects:
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
Online Access:Get full text
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Summary: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.
Bibliography:http://dx.doi.org/10.1080/01621459.2012.664527
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ISSN:1537-274X
0162-1459
1537-274X
DOI:10.1080/01621459.2012.664527