Estimation of parameters of regularly varying distributions on convex cones

Youri Davydov (1) , Shuyan Liu (2)

1 LPP - Laboratoire Paul Painlevé - UMR 8524
2 Institut de Statistique, Biostatistique et Sciences Actuarielles (ISBA)

The objective of this paper is to extend an estimation method of parameters of the stable distributions in $\rd$ to the regularly varying tails distributions in an arbitrary cone. The consistency and the asymptotic normality of estimators are proved. The sampling method of regrouping is modified to optimize the rate of convergence of estimators.

Mots clés: regularly varying distributions; estimation of parameters; stable distributions; spectral measure

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

Youri Davydov, Shuyan Liu. Estimation of parameters of regularly varying distributions on convex cones. 2010. ⟨hal-00519767⟩