LAN property for some fractional type Brownian motion

Serge Cohen (1) , Fabrice Gamboa (1) , Céline Lacaux (2, 3) , Jean-Michel Loubes (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 BIGS - Biology, genetics and statistics
3 IECL - Institut Élie Cartan de Lorraine

We study asymptotic expansion of the likelihood of a certain class of Gaussian processes characterized by their spectral density $f_\theta$. We consider the case where $f_\theta\PAR{x} \sim_{x\to 0} \ABS{x}^{-\al(\theta)}L_\theta(x)$ with $L_\theta$ a slowly varying function and $\al\PAR{\theta}\in (-\infty,1)$. We prove LAN property for these models which include in particular fractional Brownian motion %$B^\alpha_t,\: \alpha \geq 1/2$ or ARFIMA processes.

Mots clés: Fractional Brownian motion; Asymptotic Statistics

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Serge Cohen, Fabrice Gamboa, Céline Lacaux, Jean-Michel Loubes. LAN property for some fractional type Brownian motion. ALEA : Latin American Journal of Probability and Mathematical Statistics, 2013, 10 (1), pp.91-106. ⟨10.48550/arXiv.1111.1077⟩. ⟨hal-00638121⟩