Non-asymptotic Estimates for Markov Transition Matrices via Spectral Gap Methods

De Huang; Xiangyuan Li

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arXiv · 2408.05963

Non-asymptotic Estimates for Markov Transition Matrices via Spectral Gap Methods

De Huang·Xiangyuan Li

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Abstract

We establish non-asymptotic error bounds for the classical Maximal Likelihood Estimation of the transition matrix of a given Markov chain. Meanwhile, in the reversible case, we propose a new reversibility-preserving online Symmetric Counting Estimation of the transition matrix with non-asymptotic deviation bounds. Our analysis is based on a convergence study of certain Markov chains on the length-2 path spaces induced by the original Markov chain.

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De Huang, Xiangyuan Li. 2024-08-12. Non-asymptotic Estimates for Markov Transition Matrices via Spectral Gap Methods. https://arxiv.org/abs/2408.05963

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