Truncated sequential guaranteed estimation for the Cox-Ingersoll-Ross models
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866913780563181568 |
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| author | Alaya, Mohamed Ben Ngô, Thi-Bao Trâm Pergamenchtchikov, Serguei |
| author_facet | Alaya, Mohamed Ben Ngô, Thi-Bao Trâm Pergamenchtchikov, Serguei |
| contents | The drift sequential parameter estimation problems for the Cox-Ingersoll-Ross (CIR) processes under the limited duration of observation are studied. Truncated sequential estimation methods for both scalar and {two}-dimensional parameter cases are proposed. In the non-asymptotic setting, for the proposed truncated estimators, the properties of guaranteed mean-square estimation accuracy are established. In the asymptotic formulation, when the observation time tends to infinity, it is shown that the proposed sequential procedures are asymptotically optimal among all possible sequential and non-sequential estimates with an average estimation time less than the fixed observation duration. It also turned out that asymptotically, without degrading the estimation quality, they significantly reduce the observation duration compared to classical non-sequential maximum likelihood estimations based on a fixed observation duration. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_04923 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Truncated sequential guaranteed estimation for the Cox-Ingersoll-Ross models Alaya, Mohamed Ben Ngô, Thi-Bao Trâm Pergamenchtchikov, Serguei Statistics Theory Primary 44A10, 60F05, Secondary 62F12, 65C05 The drift sequential parameter estimation problems for the Cox-Ingersoll-Ross (CIR) processes under the limited duration of observation are studied. Truncated sequential estimation methods for both scalar and {two}-dimensional parameter cases are proposed. In the non-asymptotic setting, for the proposed truncated estimators, the properties of guaranteed mean-square estimation accuracy are established. In the asymptotic formulation, when the observation time tends to infinity, it is shown that the proposed sequential procedures are asymptotically optimal among all possible sequential and non-sequential estimates with an average estimation time less than the fixed observation duration. It also turned out that asymptotically, without degrading the estimation quality, they significantly reduce the observation duration compared to classical non-sequential maximum likelihood estimations based on a fixed observation duration. |
| title | Truncated sequential guaranteed estimation for the Cox-Ingersoll-Ross models |
| topic | Statistics Theory Primary 44A10, 60F05, Secondary 62F12, 65C05 |
| url | https://arxiv.org/abs/2504.04923 |