Regularization after retention in ultrahigh dimensional linear regression models

Haolei Weng, Yang Feng, Xingye Qiao

Research output: Contribution to journalArticlepeer-review


In ultrahigh dimensional setting, independence screening has been both theoretically and empirically proved a useful variable selection framework with low computation cost. In this work, we propose a two-step framework using marginal information in a different fashion than independence screening. In particular, we retain significant variables rather than screening out irrelevant ones. The method is shown to be model selection consistent in the ultrahigh dimensional linear regression model. To improve the finite sample performance, we then introduce a three-step version and characterize its asymptotic behavior. Simulations and data analysis show advantages of our method over independence screening and its iterative variants in certain regimes.

Original languageEnglish (US)
Pages (from-to)387-407
Number of pages21
JournalStatistica Sinica
Issue number1
StatePublished - 2019


  • Independence screening
  • Lasso
  • Penalized least square
  • Retention
  • Selection consistency
  • Variable selection

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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