A moment estimator for the index of an extreme-value distribution

On generalise l'estimateur bien connu de Hill de l'indice d'une fonction de reparatition avec queue de variation reguliere a une estimation de l'indice d'une loi de valeurs extremes. On demontre la convergence et la normalite asymptotique. On utilise l'estimateur pour certaines estimations comme celle d'une quantile elevee et d'un point d'extremite

[1]  L. Haan,et al.  On the Estimation of the Extreme-Value Index and Large Quantile Estimation , 1989 .

[2]  Paul Deheuvels,et al.  Almost sure convergence of the Hill estimator , 1988, Mathematical Proceedings of the Cambridge Philosophical Society.

[3]  Variation with Remainder , 1988 .

[4]  Laws of the Iterated Logarithm in the Tails for Weighted Uniform Empirical Processes , 1988 .

[5]  Richard L. Smith.  Estimating tails of probability distributions , 1987 .

[6]  H. Joe.  Estimation of quantiles of the maximum of N observations , 1987 .

[7]  J. Beirlant,et al.  Asymptotics of Hill's estimator , 1986 .

[8]  D. Mason,et al.  Central limit theorems for sums of extreme values , 1985, Mathematical Proceedings of the Cambridge Philosophical Society.

[9]  E. Haeusler,et al.  On Asymptotic Normality of Hill's Estimator for the Exponent of Regular Variation , 1985 .

[10]  Sidney I. Resnick,et al.  Tail estimates motivated by extreme-value theory , 1984, Advances in Applied Probability.

[11]  Laurens de Haan,et al.  Slow Variation and Characterization of Domains of Attraction , 1984 .

[12]  Richard L. Smith.  Uniform rates of convergence in extreme-value theory , 1982, Advances in Applied Probability.

[13]  D. Mason.  Laws of Large Numbers for Sums of Extreme Values , 1982 .

[14]  Peter Hall,et al.  On Estimating the Endpoint of a Distribution , 1982 .

[15]  J. Wellner.  Limit theorems for the ratio of the empirical distribution function to the true distribution function , 1978 .

[16]  B. M. Hill,et al.  A Simple General Approach to Inference About the Tail of a Distribution , 1975 .

[17]  L. Haan,et al.  Residual Life Time at Great Age , 1974 .

[18]  Kai Lai Chung,et al.  A Course in Probability Theory , 1949 .