Oracle estimation of parametric models under boundary constraints

Kin Yau Wong, Yair Goldberg, Jason P. Fine

Research output: Contribution to journalArticlepeer-review

Abstract

In many classical estimation problems, the parameter space has a boundary. In most cases, the standard asymptotic properties of the estimator do not hold when some of the underlying true parameters lie on the boundary. However, without knowledge of the true parameter values, confidence intervals constructed assuming that the parameters lie in the interior are generally over-conservative. A penalized estimation method is proposed in this article to address this issue. An adaptive lasso procedure is employed to shrink the parameters to the boundary, yielding oracle inference which adapt to whether or not the true parameters are on the boundary. When the true parameters are on the boundary, the inference is equivalent to that which would be achieved with a priori knowledge of the boundary, while if the converse is true, the inference is equivalent to that which is obtained in the interior of the parameter space. The method is demonstrated under two practical scenarios, namely the frailty survival model and linear regression with order-restricted parameters. Simulation studies and real data analyses show that the method performs well with realistic sample sizes and exhibits certain advantages over standard methods.

Original languageEnglish
Pages (from-to)1173-1183
Number of pages11
JournalBiometrics
Volume72
Issue number4
DOIs
StatePublished - 1 Dec 2016

Bibliographical note

Publisher Copyright:
© 2016, The International Biometric Society

Keywords

  • Constrained parameter space
  • Maximum likelihood
  • Order restrictions
  • Penalization
  • Selection consistency

ASJC Scopus subject areas

  • General Agricultural and Biological Sciences
  • Applied Mathematics
  • General Biochemistry, Genetics and Molecular Biology
  • General Immunology and Microbiology
  • Statistics and Probability

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