Non-asymptotic Estimates for Markov Transition Matrices via Spectral Gap Methods
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917063153418240 |
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| author | Huang, De Li, Xiangyuan |
| author_facet | Huang, De Li, Xiangyuan |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2408_05963 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Non-asymptotic Estimates for Markov Transition Matrices via Spectral Gap Methods Huang, De Li, Xiangyuan Statistics Theory Probability 60J10, 37A25, 62M05 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. |
| title | Non-asymptotic Estimates for Markov Transition Matrices via Spectral Gap Methods |
| topic | Statistics Theory Probability 60J10, 37A25, 62M05 |
| url | https://arxiv.org/abs/2408.05963 |