A note on concentration inequalities for the overlapped batch mean variance estimators for Markov chains
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866916735127388160 |
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| author | Moulines, Eric Naumov, Alexey Samsonov, Sergey |
| author_facet | Moulines, Eric Naumov, Alexey Samsonov, Sergey |
| contents | In this paper, we study the concentration properties of quadratic forms associated with Markov chains using the martingale decomposition method introduced by Atchadé and Cattaneo (2014). In particular, we derive concentration inequalities for the overlapped batch mean (OBM) estimators of the asymptotic variance for uniformly geometrically ergodic Markov chains. Our main result provides an explicit control of the $p$-th moment of the difference between the OBM estimator and the asymptotic variance of the Markov chain with explicit dependence upon $p$ and mixing time of the underlying Markov chain. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_08456 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A note on concentration inequalities for the overlapped batch mean variance estimators for Markov chains Moulines, Eric Naumov, Alexey Samsonov, Sergey Probability Statistics Theory Machine Learning 60J10, 60J22, 62M10 In this paper, we study the concentration properties of quadratic forms associated with Markov chains using the martingale decomposition method introduced by Atchadé and Cattaneo (2014). In particular, we derive concentration inequalities for the overlapped batch mean (OBM) estimators of the asymptotic variance for uniformly geometrically ergodic Markov chains. Our main result provides an explicit control of the $p$-th moment of the difference between the OBM estimator and the asymptotic variance of the Markov chain with explicit dependence upon $p$ and mixing time of the underlying Markov chain. |
| title | A note on concentration inequalities for the overlapped batch mean variance estimators for Markov chains |
| topic | Probability Statistics Theory Machine Learning 60J10, 60J22, 62M10 |
| url | https://arxiv.org/abs/2505.08456 |