Post selection shrinkage estimation for high-dimensional data analysis

UNCG Author/Contributor (non-UNCG co-authors, if there are any, appear on document)
Xiaoli Gao, Associate Professor (Creator)
The University of North Carolina at Greensboro (UNCG )
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Abstract: In high-dimensional data settings where p » n, many penalized regularization approaches were studied for simultaneous variable selection and estimation. However, with the existence of covariates with weak effect, many existing variable selection methods, including Lasso and its generations, cannot distinguish covariates with weak and no contribution. Thus, prediction based on a subset model of selected covariates only can be inefficient. In this paper, we propose a post selection shrinkage estimation strategy to improve the prediction performance of a selected subset model. Such a post selection shrinkage estimator (PSE) is data adaptive and constructed by shrinking a post selection weighted ridge estimator in the direction of a selected candidate subset. Under an asymptotic distributional quadratic risk criterion, its prediction performance is explored analytically. We show that the proposed post selection PSE performs better than the post selection weighted ridge estimator. More importantly, it improves the prediction performance of any candidate subset model selected from most existing Lasso-type variable selection methods significantly. The relative performance of the post selection PSE is demonstrated by both simulation studies and real-data analysis.

Additional Information

Applied Stochastic Models in Business and Industry, 33(2), 97-120
Language: English
Date: 2017
asymptotic risk, lasso, ridge regression, (positive) shrinkage estimation, post selection, sparse model

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