Local Asymptotic Normality Complexity Arising in a Parametric Statistical Lévy Model
We consider statistical experiments associated with a Lévy process X=Xtt≥0 observed along a deterministic scheme iun, 1≤i≤n. We assume that under a probability ℙθ, the r.v. Xt, t>0, has a probability density function >o, which is regular enough relative to a parameter θ∈0,∞. We prove that the...
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| Format: | Article |
| Language: | English |
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Hindawi-Wiley
2021-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2021/3143324 |
| _version_ | 1798034347411898368 |
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| author | Wissem Jedidi |
| author_facet | Wissem Jedidi |
| author_sort | Wissem Jedidi |
| collection | DOAJ |
| description | We consider statistical experiments associated with a Lévy process X=Xtt≥0 observed along a deterministic scheme iun, 1≤i≤n. We assume that under a probability ℙθ, the r.v. Xt, t>0, has a probability density function >o, which is regular enough relative to a parameter θ∈0,∞. We prove that the sequence of the associated statistical models has the LAN property at each θ, and we investigate the case when X is the product of an unknown parameter θ by another Lévy process Y with known characteristics. We illustrate the last results by the case where Y is attracted by a stable process. |
| first_indexed | 2024-04-11T20:43:02Z |
| format | Article |
| id | doaj.art-edc49d8411c042458367c464f34dd9e3 |
| institution | Directory Open Access Journal |
| issn | 1099-0526 |
| language | English |
| last_indexed | 2024-04-11T20:43:02Z |
| publishDate | 2021-01-01 |
| publisher | Hindawi-Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj.art-edc49d8411c042458367c464f34dd9e32022-12-22T04:04:09ZengHindawi-WileyComplexity1099-05262021-01-01202110.1155/2021/3143324Local Asymptotic Normality Complexity Arising in a Parametric Statistical Lévy ModelWissem Jedidi0Department of Statistics and ORWe consider statistical experiments associated with a Lévy process X=Xtt≥0 observed along a deterministic scheme iun, 1≤i≤n. We assume that under a probability ℙθ, the r.v. Xt, t>0, has a probability density function >o, which is regular enough relative to a parameter θ∈0,∞. We prove that the sequence of the associated statistical models has the LAN property at each θ, and we investigate the case when X is the product of an unknown parameter θ by another Lévy process Y with known characteristics. We illustrate the last results by the case where Y is attracted by a stable process.http://dx.doi.org/10.1155/2021/3143324 |
| spellingShingle | Wissem Jedidi Local Asymptotic Normality Complexity Arising in a Parametric Statistical Lévy Model Complexity |
| title | Local Asymptotic Normality Complexity Arising in a Parametric Statistical Lévy Model |
| title_full | Local Asymptotic Normality Complexity Arising in a Parametric Statistical Lévy Model |
| title_fullStr | Local Asymptotic Normality Complexity Arising in a Parametric Statistical Lévy Model |
| title_full_unstemmed | Local Asymptotic Normality Complexity Arising in a Parametric Statistical Lévy Model |
| title_short | Local Asymptotic Normality Complexity Arising in a Parametric Statistical Lévy Model |
| title_sort | local asymptotic normality complexity arising in a parametric statistical levy model |
| url | http://dx.doi.org/10.1155/2021/3143324 |
| work_keys_str_mv | AT wissemjedidi localasymptoticnormalitycomplexityarisinginaparametricstatisticallevymodel |