Post selection shrinkage estimation for high-dimensional data analysis

Xiaoli Gao, S. E. Ahmed, Yang Feng

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)97-120
Number of pages24
JournalApplied Stochastic Models in Business and Industry
Issue number2
StatePublished - Mar 1 2017


  • (positive) shrinkage estimation
  • asymptotic risk
  • lasso
  • post selection
  • ridge regression
  • sparse model

ASJC Scopus subject areas

  • Modeling and Simulation
  • General Business, Management and Accounting
  • Management Science and Operations Research


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