Browse > Article

GENERALIZING THE REFINED PICKANDS ESTIMATOR OF THE EXTREME VALUE INDEX  

Yun, Seok-Hoon (Department of Applied Statistics, University of Suwon)
Publication Information
Journal of the Korean Statistical Society / v.33, no.3, 2004 , pp. 339-351 More about this Journal
Abstract
In this paper we generalize and improve the refined Pickands estimator of Drees (1995) for the extreme value index. The finite-sample performance of the refined Pickands estimator is not good particularly when the sample size n is small. For each fixed k = 1,2,..., a new estimator is defined by a convex combination of k different generalized Pickands estimators and its asymptotic normality is established. Optimal weights defining the estimator are also determined to minimize the asymptotic variance of the estimator. Finally, letting k depend upon n, we see that the resulting estimator has a better finite-sample behavior as well as a better asymptotic efficiency than the refined Pickands estimator.
Keywords
Extreme value index; refined Pickands estimator; asymptotic normality; adaptive estimator;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
연도 인용수 순위
1 BLOOMFIELD, P. J., ROYLE, J. A., STEINBER, L. J. AND YANG, Q. (1996). 'Accounting for meteorological effects in measuring urban ozone levels and trends', Atmospheric Environment, 30, 3067-3077   DOI   ScienceOn
2 DE HAAN, L. AND STADTMULLER, U. (1996). 'Generalized regular variation of second order', Journal of the Australian Mathematical Society, A61, 381-395
3 FALK, M. (1994). 'Efficiency of convex combinations of Pickands estimator of the extreme value index', Journal of Nonparametric Statistics, 4, 133-147
4 PEREIRA, T. T. (1994). 'Second order behavior of domains of attraction and the bias of generalized Pickands' estimator', In Extreme Value Theory and Applications Ⅲ (J. Galambos, J. Lechner and E. Simiu, eds.), 165-177, NIST
5 SMITH, R. L. (1987). ;'Estimating tails of probability distributions', The Annals of Statistics, 15, 1174-1207   DOI   ScienceOn
6 DREES, H. (1995). 'Refined Pickands estimators of the extreme value index', The Annals of Statistics, 23, 2059-2080   DOI   ScienceOn
7 HILL, B. M. (1975). 'A simple general approach to inference about the tail of a distribution', The Annals of Statistics, 3, 1163-1174   DOI   ScienceOn
8 YUN, S. (2002a). 'On a generalized Pickands estimator of the extreme value index', Journal of Statistical Planning and Inference, 102, 389-409   DOI   ScienceOn
9 DEKKERS, A. L. M., EINMAHL, J. H. J. AND DE HAAN, L. (1989). 'A moment estimator for the index of an extreme-value distribution', The Annals of Statistics, 17, 1833-1855   DOI   ScienceOn
10 YUN, S. (2002b). 'Minimax choice and convex combinations of generalized Pickands estimator of the extreme value index', Journal of the Korean Statistical Society, 31, 315-328
11 PICKANDS, J. (1975). 'Statistical inference using extreme order statistics', The Annals of Statistics, 3, 119-131   DOI   ScienceOn
12 DEKKERS, A. L. M. AND DE HAAN, L. (1989). 'On the estimation of the extreme-value index and large quantile estimation', The Annals of Statistics, 17, 1795-1832   DOI   ScienceOn
13 DE HAAN, L. (1984). 'Slow variation and characterization of domains of attraction', In Statistical Extremes and Applications (J. Tiago de Oliveira, ed.), 31-48, Reidel, Dordrecht