Notes on Sum-Tests and Independence Tests

  • Authors:

  • Bruno Bauwens;Sebastiaan A. Terwijn

  • Affiliations:

  • Ghent University, Department of Electrical Energy, Systems and Automation, Technologiepark 913, 9052, Ghent, Belgium;Radboud University Nijmegen, Department of Mathematics, P.O. Box 9010, 6500 GL, Nijmegen, The Netherlands

  • Venue:
  • Theory of Computing Systems
  • Year:
  • 2011

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Abstract

We study statistical sum-tests and independence tests, in particular for computably enumerable semimeasures on a discrete domain. Among other things, we prove that for universal semimeasures every $\Sigma ^{0}_{1}$-sum-test is bounded, but unbounded $\Pi ^{0}_{1}$-sum-tests exist, and we study to what extent the latter can be universal. For universal semimeasures, in the unary case of sum-test we leave open whether universal $\Pi ^{0}_{1}$-sum-tests exist, whereas in the binary case of independence tests we prove that they do not exist.