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

  • Yun, Seok-Hoon (Department of Applied Statistics, University of Suwon)
  • 발행 : 2005.12.01

초록

In this paper we introduce an estimator of the second order parameter characterizing the tail behavior of probability distributions and prove its consistency.

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, A61, 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', 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', 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, 2, 367-404 https://doi.org/10.1023/A:1009900215680
  6. DREES, H. (1995). 'Refined Pickands estimators of the extreme value index', 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', Annals of Statistics, 3, 1163-1174 https://doi.org/10.1214/aos/1176343247
  9. PICKANDS, J. (1975). 'Statistical inference using extreme order statistics', Annals of Statistics, 3, 11-131
  10. SERFLING, R.J. (1980). Approximation Theorems of Mathematical Statistics, John Wiley & Sons, New York
  11. YUN, S. (2002). 'On a generalized Pickands estimator of the extreme value index', Journal of Statistical Planning and Inference, 102, 38-409