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Non-asymptotic Estimates for Markov Transition Matrices v...
[Submitted on 12 Aug 2024 (v1), last revised 5 Aug 2026 (this ve · 2024-08-12 · via math.ST updates on arXiv.org

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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.

Submission history

From: Xiangyuan Li [view email]
[v1] Mon, 12 Aug 2024 07:28:27 UTC (494 KB)
[v2] Mon, 12 May 2025 11:21:40 UTC (572 KB)
[v3] Thu, 6 Nov 2025 09:04:22 UTC (183 KB)
[v4] Wed, 5 Aug 2026 06:26:51 UTC (164 KB)

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