Confidence Region and Intervals for Sparse Penalized Regression Using Variational Inequality Techniques

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Last Modified
  • March 19, 2019
Creator
  • Yin, Liang
    • Affiliation: College of Arts and Sciences, Department of Statistics and Operations Research
Abstract
  • With the abundance of large data, sparse penalized regression techniques are commonly used in data analysis due to the advantage of simultaneous variable selection and prediction. By introducing biases on the estimators, sparse penalized regression methods can often select a simpler model than unpenalized regression. A number of convex as well as non-convex penalties have been proposed in the literature to achieve sparsity. Despite intense work in this area, it remains unclear on how to perform valid inference for sparse penalized regression with a general penalty. In this work, by making use of state-of-the-art optimization tools in variational inequality theory, we propose a unified framework to construct confidence intervals for sparse penalized regression with a wide range of penalties, including the well-known least absolute shrinkage and selection operator (LASSO) penalty and the minimax concave penalty (MCP). We study the inference for two types of parameters: the parameters under the population version of the penalized regression and the parameters in the underlying linear model. Theoretical convergence properties of the proposed methods are obtained. Simulated and real data examples are presented to demonstrate the validity and effectiveness of the proposed inference procedure.
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Rights statement
  • In Copyright
Advisor
  • Zhang, Kai
  • Provan, Scott
  • Liu, Yufeng
  • Budhiraja, Amarjit
  • Lu, Shu
Degree
  • Doctor of Philosophy
Degree granting institution
  • University of North Carolina at Chapel Hill Graduate School
Graduation year
  • 2015
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Place of publication
  • Chapel Hill, NC
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  • There are no restrictions to this item.
Date uploaded
  • August 25, 2015

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