Inference after model selection

Xiaotong Shen, Hsin Cheng Huang, Jimmy Ye

Research output: Contribution to journalArticlepeer-review

31 Scopus citations


Typical modeling strategies involve model selection, which has a significant effect on inference of estimated parameters. Common practice is to use a selected model ignoring uncertainty introduced by the process of model selection. This could yield overoptimistic inferences, resulting in false discovery. In this article we develop a general methodology via optimal approximation for estimating the mean and variance of complex statistics that involve the process of model selection. This allows us to make approximately unbiased inferences, taking into account the selection process. We examine the operating characteristics of the proposed methodology via asymptotic analyses and simulations. These results show that the proposed methodology yields correct inferences and outperforms common alternatives.

Original languageEnglish (US)
Pages (from-to)751-762
Number of pages12
JournalJournal of the American Statistical Association
Issue number467
StatePublished - Sep 2004

Bibliographical note

Funding Information:
Xiaotong Shen is Professor, School of Statistics, University of Minnesota, Minneapolis, MN 55455 (E-mail: Hsin-Cheng Huang is Associate Research Fellow, Institute of Statistical Science, Academia Sinica, Taipei 115, Taiwan (E-mail: Jimmy Ye is Associate Professor, Stan Ross Department of Accountancy, Baruch College, City University of New York, NY 10010 (E-mail: Shen was supported in part by National Science Foundation grants IIS-0328802 and DMS-00-72635. Ye was supported by the Zicklin School of Business, Baruch College. The authors thank the editor, the associate editor, and two anonymous referees for helpful comments and suggestions.


  • Bootstrap
  • Nonparametric
  • Parametric
  • Variable selection
  • Wavelet thresholding

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