Finite-Sample Risk Bounds for Maximum Likelihood Estimation with Arbitrary Penalties

W. D. Brinda, Jason M. Klusowski

Research output: Contribution to journalArticle

Abstract

The minimum description length two-part coding index of resolvability provides a finite-sample upper bound on the statistical risk of penalized likelihood estimators over countable models. However, the bound does not apply to unpenalized maximum likelihood estimation or procedures with exceedingly small penalties. In this paper, we point out a more general inequality that holds for arbitrary penalties. In addition, this approach makes it possible to derive exact risk bounds of order 1/n for iid parametric models, which improves on the order (log n)/n resolvability bounds. We conclude by discussing implications for adaptive estimation.

Original languageEnglish (US)
Pages (from-to)2727-2741
Number of pages15
JournalIEEE Transactions on Information Theory
Volume64
Issue number4
DOIs
StatePublished - Apr 2018

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All Science Journal Classification (ASJC) codes

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences

Keywords

  • Penalized likelihood estimation
  • codelength
  • minimum description length
  • redundancy
  • statistical risk

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