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On the ααα-lazy version of Markov chains in estimation and testing problems

20 May 2021
S. Fried
Geoffrey Wolfer
ArXiv (abs)PDFHTML
Abstract

Given access to a single long trajectory generated by an unknown irreducible Markov chain MMM, we simulate an α\alphaα-lazy version of MMM 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 [2015] and defined for ergodic Markov chains may be given a meaning already in the case of irreducible but possibly periodic Markov chains.

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