Journal of the Korean Statistical Society

  • 제35권1호
  • /
  • Pages.91-103
  • /
  • 2006
  • /
  • 1226-3192(pISSN)
  • /
  • 2005-2863(eISSN)
한국통계학회 (The Korean Statistical Society)
권호 표지

ESTIMATION OF THE SECOND ORDER PARAMETER CHARACTERIZING THE TAIL BEHAVIOR OF PROBABILITY DISTRIBUTIONS: ASYMPTOTIC NORMALITY

  • Yun Seok-Hoon (Department of Applied Statistics, University of Suwon)
  • 발행 : 2006.03.01
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

Yun (2005) introduced an estimator of the second order parameter characterizing the tail behavior of probability distributions and proved its consistency. In this paper we prove its asymptotic normality under a third order condition.

키워드

참고문헌

  1. 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
  2. DE HAAN, L. AND STADTMULLER, U. (1996). 'Generalized regular variation of second order', Journal of the Australian Mathematical Society. Ser. A, 61, 381-395 https://doi.org/10.1017/S144678870000046X
  3. 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 https://doi.org/10.1214/aos/1176347396
  4. 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 https://doi.org/10.1214/aos/1176347397
  5. DRAISMA, G., DE HAAN, L., PENG, L. AND PEREIRA, T. T. (1999). 'A bootstrap-based method to achieve optimality in estimating the extreme-value index', Extremes, Engineering and Economics, 2, 367-404 https://doi.org/10.1023/A:1009900215680
  6. DREES, H. (1995). 'Refined Pickands estimators of the extreme value index', The Annals of Statistics, 23, 2059-2080 https://doi.org/10.1214/aos/1034713647
  7. GOMES, M. I., DE HAAN, L. AND PENG, L. (2002). 'Semi-parametric estimation of the second order parameter in statistics of extremes', Extremes, 5, 387-414 https://doi.org/10.1023/A:1025128326588
  8. HILL, B. M. (1975). 'A simple general approach to inference about the tail of a distribution', The Annals of Statistics, 3, 1163-1174 https://doi.org/10.1214/aos/1176343247
  9. PICKANDS, J. (1975). 'Statistical inference using extreme order statistics', The Annals of Statistics, 3, 119-131 https://doi.org/10.1214/aos/1176343003
  10. YUN, S. (2002). 'On a generalized Pickands estimator of the extreme value index', Journal of Statistical Planning and Inference, 102, 389-409 https://doi.org/10.1016/S0378-3758(01)00100-8
  11. YUN, S. (2005). 'Estimation of the second order parameter characterizing the tail behavior of probability distributions: Consistency', Journal of the Korean Statistical Society, 34, 273-280