OPTIMAL CHOICE OF SAMPLE FRACTION IN EXTREME-VALUE ESTIMATION

被引:76
|
作者
DEKKERS, ALM [1 ]
DEHAAN, L [1 ]
机构
[1] ERASMUS UNIV ROTTERDAM,3000 DR ROTTERDAM,NETHERLANDS
关键词
EXTREME-VALUE THEORY; ORDER STATISTICS; ASYMPTOTIC NORMALITY; MEAN SQUARED ERROR; REGULAR VARIATION; PI-VARIATION; INVERSE COMPLEMENTARY FUNCTION;
D O I
10.1006/jmva.1993.1078
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 the asymptotic bias of the moment estimator γ̂n for the extreme-value index γ ∈ R under quite natural and general conditions on the underlying distribution function. Furthermore the optimal choice for the sample franction in estimating γ is considered by minimizing the mean squared error of γ̂n - γ. The results cover all three limiting types of extreme-value theory. The connection between statistics and regular variation and Π-variation is handled in a systematic way. © 1993 Academic Press, Inc.
引用
收藏
页码:173 / 195
页数:23
相关论文
共 50 条
  • [1] Selecting the optimal sample fraction in univariate extreme value estimation
    Drees, H
    Kaufmann, E
    [J]. STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 1998, 75 (02) : 149 - 172
  • [2] ON THE ESTIMATION OF THE EXTREME-VALUE INDEX AND LARGE QUANTILE ESTIMATION
    DEKKERS, ALM
    DEHAAN, L
    [J]. ANNALS OF STATISTICS, 1989, 17 (04): : 1795 - 1832
  • [3] Extreme-Value Theorems for Optimal Multidimensional Pricing
    Cai, Yang
    Daskalakis, Constantinos
    [J]. 2011 IEEE 52ND ANNUAL SYMPOSIUM ON FOUNDATIONS OF COMPUTER SCIENCE (FOCS 2011), 2011, : 522 - 531
  • [4] Nonparametric estimation of multivariate extreme-value copulas
    Gudendorf, Gordon
    Segers, Johan
    [J]. JOURNAL OF STATISTICAL PLANNING AND INFERENCE, 2012, 142 (12) : 3073 - 3085
  • [5] BAYES ESTIMATION OF THE EXTREME-VALUE RELIABILITY FUNCTION
    LYE, LM
    HAPUARACHCHI, KP
    RYAN, S
    [J]. IEEE TRANSACTIONS ON RELIABILITY, 1993, 42 (04) : 641 - 644
  • [6] Modeling Extreme Events: Sample Fraction Adaptive Choice in Parameter Estimation
    Neves, Manuela
    Gomes, Ivette
    Figueiredo, Fernanda
    Gomes, Dora Prata
    [J]. NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM 2012), VOLS A AND B, 2012, 1479 : 1110 - 1113
  • [7] Modeling extreme events: Sample fraction adaptive choice in parameter estimation
    Neves M.M.
    Gomes M.I.
    Figueiredo F.
    Gomes D.P.
    [J]. Journal of Statistical Theory and Practice, 2015, 9 (1) : 184 - 199
  • [8] Mixture of extreme-value distributions: identifiability and estimation
    Otiniano, C. E. G.
    Goncalves, C. R.
    Dorea, C. C. Y.
    [J]. COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, 2017, 46 (13) : 6528 - 6542
  • [9] ESTIMATION AND TESTING OF QUANTILES OF THE EXTREME-VALUE DISTRIBUTION
    HASSANEIN, KM
    SALEH, AKME
    BROWN, EF
    [J]. JOURNAL OF STATISTICAL PLANNING AND INFERENCE, 1986, 14 (03) : 389 - 400
  • [10] Optimal choice of sample fraction in univariate financial tail index estimation
    Cheong, Chin Wen
    [J]. JOURNAL OF APPLIED STATISTICS, 2010, 37 (12) : 2043 - 2056