Berry-Esseen Bounds for Statistics of Non-Stationary, $ϕ$-Mixing Random Variables
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866910103037280256 |
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| author | Williams, Brendan Hafouta, Yeor |
| author_facet | Williams, Brendan Hafouta, Yeor |
| contents | Using a modification of Stein's method, we generalize the results of Bentkus, G{ö}tze, and Tikhomirov \cite{bentkus1997berry} to obtain Berry-Esseen bounds for a broad class of statistics of sequences of $ϕ$-mixing, non-stationary random variables with polynomial mixing rates. %and linear variance.
We then consider applications of this theorem to ensure Berry-Esseen rates for various classes of non-stationary $ϕ$-mixing random variables, including rates for a general class of processes of $ϕ$-mixing random variables satisfying an aggregate third moment bound. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_03712 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Berry-Esseen Bounds for Statistics of Non-Stationary, $ϕ$-Mixing Random Variables Williams, Brendan Hafouta, Yeor Probability Statistics Theory Using a modification of Stein's method, we generalize the results of Bentkus, G{ö}tze, and Tikhomirov \cite{bentkus1997berry} to obtain Berry-Esseen bounds for a broad class of statistics of sequences of $ϕ$-mixing, non-stationary random variables with polynomial mixing rates. %and linear variance. We then consider applications of this theorem to ensure Berry-Esseen rates for various classes of non-stationary $ϕ$-mixing random variables, including rates for a general class of processes of $ϕ$-mixing random variables satisfying an aggregate third moment bound. |
| title | Berry-Esseen Bounds for Statistics of Non-Stationary, $ϕ$-Mixing Random Variables |
| topic | Probability Statistics Theory |
| url | https://arxiv.org/abs/2604.03712 |