Local Asymptotic Normality complexity arising in a parametric statistical Lévy Model
We consider statistical experiments associated with a L\'evy process $X$ observed along a deterministic scheme ($ i \, u_n, \,1 \leq i \leq n).$ We assume that under a probability $ \po,$ at each $t>0$, $X_t$ has a density $\gto $ regular enough relative to a parameter $\theta \in (0,+\infty).$ We prove that the sequence of the associated statistical models has the LAN property at each $\theta,$ and we investigate the case when $X$ is the product of an unknown parameter $\theta$ by an another L\'evy process $Y$ with known characteristics, by giving examples with $Y$ attracted by a stable process.
S. Bridaa, W. Jedidi and H. Sendov: Generalized unimodality and subordinators, with applications to stable laws and to the Mittag-Leffler function
W. Jedidi: Regularity of some models…
In this paper we provide some new properties that are complementary to the book
of Schilling-Song-Vondraek
We consider statistical experiments associated with a L\'evy process $X$ observed along a deterministic scheme ($ i \, u_n, \,1 \leq i \leq n).$ We assume that under a probability $ \po,$ at…