Robust high-dimensional data analysis using a weight shrinkage rule

UNCG Author/Contributor (non-UNCG co-authors, if there are any, appear on document)
Bin Luo (Creator)
The University of North Carolina at Greensboro (UNCG )
Web Site:
Xiaoli Gao

Abstract: In high-dimensional settings, a penalized least squares approach may lose its efficiency in both estimation and variable selection due to the existence of either outliers or heteroscedasticity. In this thesis, we propose a novel approach to perform robust high-dimensional data analysis in a penalized weighted least square framework. The main idea is to relate the irregularity of each observation to a weight vector and obtain the outlying status data-adaptively using a weight shrinkage rule. By usage of L-1 type regularization on both the coefficients and weight vectors, the proposed method is able to perform simultaneous variable selection and outliers detection efficiently. Eventually, this procedure results in estimators with potentially strong robustness and non-asymptotic consistency. We provide a unified link between the weight shrinkage rule and a robust M-estimation in general settings. We also establish the non-asymptotic oracle inequalities for the joint estimation of both the regression coefficients and weight vectors. These theoretical results allow the number of variables to far exceed the sample size. The performance of the proposed estimator is demonstrated in both simulation studies and real examples.

Additional Information

Language: English
Date: 2016
Adaptive lasso, M-estimation, Oracle inequality, Weight least squares, Weight shrinkage
Dimensional analysis $x Data processing
Estimation theory
Least squares

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