Simulation-based consistent inference for biased working model of non-sparse high-dimensional linear regression

Lu Lin*, Feng Li, Lixing ZHU

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review


Variable selection in regression analysis is of importance because it can simplify model and enhance predictability. After variable selection, however, the resulting working model may be biased when it does not contain all of significant variables. As a result, the commonly used parameter estimation is either inconsistent or needs estimating high-dimensional nuisance parameter with very strong assumptions for consistency, and the corresponding confidence region is invalid when the bias is relatively large. We in this paper introduce a simulation-based procedure to reformulate a new model so as to reduce the bias of the working model, with no need to estimate high-dimensional nuisance parameter. The resulting estimators of the parameters in the working model are asymptotic normally distributed whether the bias is small or large. Furthermore, together with the empirical likelihood, we build simulation-based confidence regions for the parameters in the working model. The newly proposed estimators and confidence regions outperform existing ones in the sense of consistency.

Original languageEnglish
Pages (from-to)3780-3792
Number of pages13
JournalJournal of Statistical Planning and Inference
Issue number12
Publication statusPublished - Dec 2011

Scopus Subject Areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

User-Defined Keywords

  • Biased working model
  • Consistent inference
  • Empirical likelihood
  • High dimensional regression
  • Non-sparsity


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