Notes on Sum-Tests and Independence Tests

作者：Bauwens Bruno; Terwijn Sebastiaan A^*

来源：Theory of Computing Systems, 2011, 48(2): 247-268.

DOI：10.1007/s00224-009-9240-4

• Sum-tests
• Independence tests
• Kolmogorov complexity

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.

• 出版日期2011-2