Hypothesis testing by convex optimization

Alexander Goldenshluger, Anatoli Juditsky, Arkadi Nemirovski

Research output: Contribution to journalArticlepeer-review


We discuss a general approach to hypothesis testing. The main “building block” of the proposed construction is a test for a pair of hypotheses in the situation where each particular hypothesis states that the vector of parameters identifying the distribution of observations belongs to a convex compact set associated with the hypothesis. This test, under appropriate assumptions, is nearly optimal and is yielded by a solution to a convex optimization problem, so that the construction admits computationally efficient implementation.We further demonstrate that our assumptions are satisfied in several important and interesting applications. Finally, we show how our approach can be applied to a rather general testing problems encompassing several classical statistical settings.

Original languageEnglish
Pages (from-to)1645-1712
Number of pages68
JournalElectronic Journal of Statistics
Issue number2
StatePublished - 19 Aug 2015

Bibliographical note

Publisher Copyright:
© 2015, Institute of Mathematical Statistics. All rights reserved.


  • Composite hypothesis testing
  • Hypothesis testing
  • Nonparametric testing
  • Statistical applications of convex optimization

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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