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.
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B. Bauwens supported by a Ph.D grant of the Institute for the Promotion of Innovation through Science and Technology in Flanders (IWT-Vlaanderen).
S.A. Terwijn supported by the Austrian Science Fund FWF under project P20346-N18.
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Bauwens, B., Terwijn, S.A. Notes on Sum-Tests and Independence Tests. Theory Comput Syst 48, 247–268 (2011). https://doi.org/10.1007/s00224-009-9240-4
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DOI: https://doi.org/10.1007/s00224-009-9240-4