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On the $$\alpha $$ α -lazy version of Markov chains in estimation and testing problems

Author

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  • Sela Fried

    (Ben-Gurion University of the Negev)

Abstract

Given access to a single long trajectory generated by an unknown irreducible Markov chain M, we simulate an $$\alpha $$ α -lazy version of M which is ergodic. This enables us to generalize recent results on estimation and identity testing, that were stated for ergodic Markov chains, in a way that allows fully empirical inference. In particular, our approach shows that the pseudo spectral gap introduced by Paulin (Electron J Probab 20:32, 2015) and defined for ergodic Markov chains may be given a meaning already in the case of irreducible but possibly periodic Markov chains.

Suggested Citation

  • Sela Fried, 2023. "On the $$\alpha $$ α -lazy version of Markov chains in estimation and testing problems," Statistical Inference for Stochastic Processes, Springer, vol. 26(2), pages 413-435, July.
    • Handle: RePEc:spr:sistpr:v:26:y:2023:i:2:d:10.1007_s11203-022-09283-7
    DOI: 10.1007/s11203-022-09283-7
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