Poisson limits for U-statistics

被引：10
作者：
Dabrowski, AR
Dehling, HG
Mikosch, T
Sharipov, O
机构：
[1] Univ Ottawa, Dept Math & Stat, Ottawa, ON K1N 6N5, Canada
[2] Ruhr Univ Bochum, Fac Math, D-44780 Bochum, Germany
[3] Univ Copenhagen, Inst Math Sci, Lab Actuarial Math, DK-2100 Copenhagen, Denmark
[4] Uzbek Acad Sci, Inst Math, Dept Probabil Theory, Tashkent 700143, Uzbekistan
来源：
STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2002年 / 99卷 / 01期
关键词：
U-statistic; Poisson random measure; correlation dimension; Takens estimator; Hill estimator; stable distribution; Stein-Chen method; self-normalized sum;
D O I：
10.1016/S0304-4149(01)00153-3
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
We study Poisson limits for U-statistics with non-negative kernels. The limit theory is derived from the Poisson convergence of suitable point processes of U-statistics structure. We apply these results to derive infinite variance stable limits for U-statistics with a regularly varying kernel and to determine the index of regular variation of the left tail of the kernel. The latter is known as correlation dimension. We use the point process convergence to study the asymptotic behavior of some standard estimators of this dimension. (C) 2001 Elsevier Science B.V. All rights reserved.
引用
收藏
页码：137 / 157
页数：21
相关论文
共 22 条
  • [1] Strong laws for L- and U-statistics
    Aaronson, J
    Burton, R
    Dehling, H
    Gilat, D
    Hill, T
    Weiss, B
    [J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1996, 348 (07) : 2845 - 2866
  • [2] BARBOUR AD, 1984, J ROY STAT SOC B MET, V46, P397
  • [3] Barbour AD, 1992, Poisson approximation
  • [4] BILLINGSLEY P., 1999, Convergence of Probability Measures, V2nd, DOI 10.1002/9780470316962
  • [5] BINGHAM N. H., 1989, Regular variation
  • [6] Cressie N, 1993, STAT SPATIAL DATA
  • [7] Daley D. J., 2002, INTRO THEORY POINT P
  • [8] POINT PROCESS AND PARTIAL SUM CONVERGENCE FOR WEAKLY DEPENDENT RANDOM-VARIABLES WITH INFINITE VARIANCE
    DAVIS, RA
    HSING, TL
    [J]. ANNALS OF PROBABILITY, 1995, 23 (02) : 879 - 917
  • [9] Embrechts P., 1997, MODELLING EXTREMAL E, DOI 10.1007/978-3-642-33483-2
  • [10] CHARACTERIZATION OF STRANGE ATTRACTORS
    GRASSBERGER, P
    PROCACCIA, I
    [J]. PHYSICAL REVIEW LETTERS, 1983, 50 (05) : 346 - 349
123