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...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Hindawi-Wiley
2021-01-01
|
| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2021/3143324 |
| Summary: | 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. |
|---|---|
| ISSN: | 1099-0526 |