基于分块思想的Pickands型估计量
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摘要
基于Davydov等提出的分块思想,构造一类新的Pickands型估计量,并证明其相合性和渐近正态性.
Based on the block method proposed by Davydov et al., we propose in this paper a new Pickands-type estimator. The asymptotic properties of the new estimator, such as its consistency and asymptotic normality, are derived under some regular conditions.
Based on the block method proposed by Davydov et al., we propose in this paper a new Pickands-type estimator. The asymptotic properties of the new estimator, such as its consistency and asymptotic normality, are derived under some regular conditions.
引文
[1]PICKANDS J.Statistical Inference Using Extreme Order Statistics[J].Annals of Statistics,1975,3(1):119-131.
[2]DEKKERS A L M,HAAN L D.On the Estimation of the Extreme-Value Index and Large Quantile Estimation[J].Annals of Statistics,1989,17(4):1795-1832.
[3]彭作祥.Pickands型估计的推广[J].数学学报,1997(5):759-762.
[4]PENG Z X,NADARAJAH S.The Pickands’Estimator of the Negative Extreme-Value Index[J].Acta Scicentiarum Naturalum Universitis Pekinesis,2001,37(1):12-19.
[5]DAVYDOV Y,PAULAUSKAS V,RA C∨KAUSKAS A.More on P-Stable Convex Sets in Banach Spaces[J].Journal of Theoretical Probability,2000,13(1):39-64.
[6]PAULAUSKAS V.A New Estimator for a Tail Index[J].Acta Applicandae Mathematica,2003,79(1-2):55-67.
[7]QI Y C.On the Tail Index of a Heavy Tailed Distribution[J].Annals of the Institute of Statistical Mathematics,2010,62(2):277-298.
[8]VAI CIULIS M.Local-Maximum-Based Tail Index Estimator[J].Lithuanian Mathematical Journal,2014,54(4):503-526.
[9]PAULAUSKAS V,VAI CIULIS M.Comparison of the Several Parameterized Estimators for the Positive Extreme Value Index[J].Journal of Statistical Computation&Simulation,2016,87(7):1342-1362.
[10]马跃,彭作祥.广义误差-帕累托分布及其在保险中的应用[J].西南大学学报(自然科学版),2017,39(1):99-102.
[11]HAAN L D.Slow Variation and Characterization of Domains of Attraction[J].Statistical Extremes and Applications,1984:31-48.
[12]MICHAILIDIS G,STOEV S.Extreme Value Theory:An Introduction[J].Technometrics,2007,49(4):491-492.
[13]RESNICK S I.A Probability Path[M].Boston:Birkhuser,1999.
[2]DEKKERS A L M,HAAN L D.On the Estimation of the Extreme-Value Index and Large Quantile Estimation[J].Annals of Statistics,1989,17(4):1795-1832.
[3]彭作祥.Pickands型估计的推广[J].数学学报,1997(5):759-762.
[4]PENG Z X,NADARAJAH S.The Pickands’Estimator of the Negative Extreme-Value Index[J].Acta Scicentiarum Naturalum Universitis Pekinesis,2001,37(1):12-19.
[5]DAVYDOV Y,PAULAUSKAS V,RA C∨KAUSKAS A.More on P-Stable Convex Sets in Banach Spaces[J].Journal of Theoretical Probability,2000,13(1):39-64.
[6]PAULAUSKAS V.A New Estimator for a Tail Index[J].Acta Applicandae Mathematica,2003,79(1-2):55-67.
[7]QI Y C.On the Tail Index of a Heavy Tailed Distribution[J].Annals of the Institute of Statistical Mathematics,2010,62(2):277-298.
[8]VAI CIULIS M.Local-Maximum-Based Tail Index Estimator[J].Lithuanian Mathematical Journal,2014,54(4):503-526.
[9]PAULAUSKAS V,VAI CIULIS M.Comparison of the Several Parameterized Estimators for the Positive Extreme Value Index[J].Journal of Statistical Computation&Simulation,2016,87(7):1342-1362.
[10]马跃,彭作祥.广义误差-帕累托分布及其在保险中的应用[J].西南大学学报(自然科学版),2017,39(1):99-102.
[11]HAAN L D.Slow Variation and Characterization of Domains of Attraction[J].Statistical Extremes and Applications,1984:31-48.
[12]MICHAILIDIS G,STOEV S.Extreme Value Theory:An Introduction[J].Technometrics,2007,49(4):491-492.
[13]RESNICK S I.A Probability Path[M].Boston:Birkhuser,1999.