Wasserstein-$1$ distance and nonuniform Berry-Esseen bound for a supercritical branching process in a random environment
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866914180453367808 |
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| author | Wu, Hao Fan, Xiequan Gao, Zhiqiang Ye, Yinna |
| author_facet | Wu, Hao Fan, Xiequan Gao, Zhiqiang Ye, Yinna |
| contents | Let $ (Z_{n})_{n\geq 0} $ be a supercritical branching process in an independent and identically distributed random environment. We establish an optimal convergence rate in the Wasserstein-$1$ distance for the process $ (Z_{n})_{n\geq 0} $, which completes a result of Grama et al. [Stochastic Process. Appl., 127(4), 1255-1281, 2017]. Moreover, an exponential nonuniform Berry-Esseen bound is also given. At last, some applications of the main results to the confidence interval estimation for the criticality parameter and the population size $Z_n$ are discussed. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2307_01084 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Wasserstein-$1$ distance and nonuniform Berry-Esseen bound for a supercritical branching process in a random environment Wu, Hao Fan, Xiequan Gao, Zhiqiang Ye, Yinna Probability Statistics Theory 60J80, 60K37, 60F05, 62E20 Let $ (Z_{n})_{n\geq 0} $ be a supercritical branching process in an independent and identically distributed random environment. We establish an optimal convergence rate in the Wasserstein-$1$ distance for the process $ (Z_{n})_{n\geq 0} $, which completes a result of Grama et al. [Stochastic Process. Appl., 127(4), 1255-1281, 2017]. Moreover, an exponential nonuniform Berry-Esseen bound is also given. At last, some applications of the main results to the confidence interval estimation for the criticality parameter and the population size $Z_n$ are discussed. |
| title | Wasserstein-$1$ distance and nonuniform Berry-Esseen bound for a supercritical branching process in a random environment |
| topic | Probability Statistics Theory 60J80, 60K37, 60F05, 62E20 |
| url | https://arxiv.org/abs/2307.01084 |