Efficient Estimation of the Canonical Dependence Function

被引：0
作者：
Michael Falk
Rolf Reiss
机构：
[1] Universität Würzburg,Institut für Angewandte Mathematik und Statistik
[2] Universität GH Siegen,Fachbereich Mathematik
来源：
Extremes | 2003年 / 6卷 / 1期
关键词：
bivariate extreme value distribution; bivariate generalized Pareto distribution; δ-neighborhood; Pickands representation; dependence function; Pickands co-ordinates; canonical dependence function; local asymptotic normality (LAN);
D O I：
10.1023/A:1026229314063
中图分类号：
学科分类号：
摘要：
The canonical dependence function θ (z), z ∈ [0,1], is introduced and studied in detail for distributions, which belong to the δ-neighborhood of a bivariate generalized Pareto distribution. We establish local asymptotic normality (LAN) of the loglikelihood function of a 2×2 table sorting of n i.i.d. observations and derive efficient estimators of θ (z) from the Hájek-LeCam Convolution Theorem. These results extend results by Falk and Reiss (2003) for the canonical dependence parameter θ (1/2) to arbitrary z ∈ (0,1).
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页码：61 / 82
页数：21
相关论文
共 22 条
[1]  
Coles S.(1999)Dependent measures for extreme value analysis Extremes 2 339-365
[2]  
Heffernan J.(1991)On the limiting behavior of the Pickands estimator for bivariate extreme value distributions Statist. Probab. Letters 12 429-439
[3]  
Tawn J.(2001)Efficiency of estimators of the dependence parameter in a class of bivariate Peaks-Over-Threshold models Statist. Probab. Letters 52 233-242
[4]  
Deheuvels P.(2002)A characterization of the rate of convergence in bivariate extreme value models Statist. Probab. Letters 59 341-351
[5]  
Falk M.(2003)Efficient estimators and LAN in canonical bivariate POT models J. Multivariate Anal. 84 190-207
[6]  
Reiss R.-D.(1960)Bivariate exponential distribution J. Amer. Statist. Assoc. 55 698-707
[7]  
Falk M.(2000)Distribution and dependence function estimation for bivariate extreme-value distributions Bernoulli 6 835-844
[8]  
Reiss R.-D.(1989)Maxima of normal random vectors: between dependence and complete dependence Statist. Probab. Letters 7 283-286
[9]  
Falk M.(1995)Approximation rates for multivariate exceedances J. Statist. Plan. Inf. 45 235-245
[10]  
Reiss R.-D.(1967)A multivariate exponential distribution J. Amer. Statist. Assoc. 62 30-44
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