Asymptotic properties of maximum likelihood estimators for determinantal point processes
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866913422258470912 |
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| author | Hu, Yaozhong Shi, Haiyi |
| author_facet | Hu, Yaozhong Shi, Haiyi |
| contents | We obtain the almost sure strong consistency and the Berry-Esseen type bound for the maximum likelihood estimator Ln of the ensemble L for determinantal point processes (DPPs), strengthening and completing previous work initiated in Brunel, Moitra, Rigollet, and Urschel [BMRU17]. Numerical algorithms of estimating DPPs are developed and simulation studies are performed. Lastly, we give explicit formula and a detailed discussion for the maximum likelihood estimator for blocked determinantal matrix of two by two submatrices and compare it with the frequency method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_00733 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Asymptotic properties of maximum likelihood estimators for determinantal point processes Hu, Yaozhong Shi, Haiyi Statistics Theory We obtain the almost sure strong consistency and the Berry-Esseen type bound for the maximum likelihood estimator Ln of the ensemble L for determinantal point processes (DPPs), strengthening and completing previous work initiated in Brunel, Moitra, Rigollet, and Urschel [BMRU17]. Numerical algorithms of estimating DPPs are developed and simulation studies are performed. Lastly, we give explicit formula and a detailed discussion for the maximum likelihood estimator for blocked determinantal matrix of two by two submatrices and compare it with the frequency method. |
| title | Asymptotic properties of maximum likelihood estimators for determinantal point processes |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2307.00733 |