A local moment type estimator for the extreme value index in regression with random covariates

Yuri Goegebeur (1) , Armelle Guillou (2) , Michael Osmann (1)

1 IMADA - Department of Mathematics and Computer Science [Odense]
2 IRMA - Institut de Recherche Mathématique Avancée

This paper deals with the nonparametric estimation of the conditional tail index in presence of random covariates. In particular, it is assumed that the conditional response distribution belongs to the max-domain of attraction of the extreme value distribution, and its tail index is estimated locally within a narrow neighborhood of the point of interest in the covariate space. The moment estimator, originally introduced in Dekkers, Einmahl, & de Haan (1989), is adjusted to the local estimation context, and its asymptotic properties are investigated under some mild conditions on the response distribution, the density function of the covariates, the kernel function, and for appropriately chosen sequences of bandwidth and threshold parameters. The finite sample performance of the proposed estimator and an alternative from the recent extreme value literature are evaluated with a small simulation study. We also illustrate the practical applicability of the estimator on the world catalogue of earthquake magnitudes.

Mots clés: Local estimation; max-domain of attraction; second order condition; tail index

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

Yuri Goegebeur, Armelle Guillou, Michael Osmann. A local moment type estimator for the extreme value index in regression with random covariates. Canadian Journal of Statistics, 2014, 42, pp.487-507. ⟨10.1002/cjs.11219⟩. ⟨hal-00845968⟩