Testing exchangeability in the batch mode with e-values and Markov alternatives

Vladimir Vovk

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arXiv · 2305.05284

Testing exchangeability in the batch mode with e-values and Markov alternatives

Vladimir Vovk

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Abstract

The topic of this paper is testing exchangeability using e-values in the batch mode, with the Markov model as alternative. The null hypothesis of exchangeability is formalized as a Kolmogorov-type compression model, and the Bayes mixture of the Markov model w.r. to the uniform prior is taken as simple alternative hypothesis. Using e-values instead of p-values leads to a computationally efficient testing procedure. In the appendixes I explain connections with the algorithmic theory of randomness and with the traditional theory of testing statistical hypotheses. In the standard statistical terminology, this paper proposes a new permutation test. This test can also be interpreted as a poor man's version of Kolmogorov's deficiency of randomness.

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BibTeX RIS

Vladimir Vovk. 2023-05-09. Testing exchangeability in the batch mode with e-values and Markov alternatives. https://arxiv.org/abs/2305.05284

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