[1]章 溢,吕凤虎.峰度与偏度系数的近似经验贝叶斯估计[J].江西师范大学学报(自然科学版),2016,40(04):358-362.
 ZHANG Yi,LYU Fenghu.The Approximate Empirical Bayesian Estimation of Kurtosis and Skewness Coefficient[J].,2016,40(04):358-362.
点击复制

峰度与偏度系数的近似经验贝叶斯估计()
分享到:

《江西师范大学学报》(自然科学版)[ISSN:1006-6977/CN:61-1281/TN]

卷:
40
期数:
2016年04期
页码:
358-362
栏目:
出版日期:
2016-09-01

文章信息/Info

Title:
The Approximate Empirical Bayesian Estimation of Kurtosis and Skewness Coefficient
作者:
章 溢吕凤虎
1.江西师范大学计算机信息工程学院,江西 南昌 330022; 2.南昌工程学院理学院,江西 南昌 330099
Author(s):
ZHANG YiLYU Fenghu
1.College of Computer Information Engineering,Jiangxi Normal University,Nanchang Jiangxi 330022,China; 2.College of Science,Nanchang Institute of Technology,Nanchang Jiangxi 330099,China
关键词:
峰度系数 偏度系数 线性贝叶斯估计 近似信度估计 超参数 经验贝叶斯估计
Keywords:
kurtosis coefficient skewness coefficient linear Bayesian estimation approximate credibility estimation supper-parameter empirical Bayes estimation
分类号:
O 211.9
文献标志码:
A
摘要:
建立了单样本数据的贝叶斯模型,给出了偏度系数和峰度系数的线性贝叶斯估计及近似信度估计.进而,将模型推广到多样本数据模型下,并讨论了近似信度估计的统计性质,比较了贝叶斯估计、线性贝叶斯估计及近似信度估计的均方误差.最后,给出了超参数的估计,得到了近似信度估计的经验贝叶斯估计,使该估计可直接运用于实际问题.
Abstract:
A Bayesian model of single sample data is established,and the Bayesian estimation,linear Bayesian estimation and approximate credibility estimation of skewness and kurtosis coefficient are given.Furthermore,the model is extended to multitude data model.In this model,the statistical properties of approximate credibility estimation are discussed,the mean square errors of Bayesian estimation,linear approximation and approximate credibility estimation are compared.Finally,the estimation of supper-parameters are given,thus the empirical Bayes estimation of approximate credibility estimation is derived,and it can be directly applied to practice.

参考文献/References:

[1] 王学民.偏度和峰度概念的认识误区 [J].统计与决策,2008(12):145-146.
[2] 邵建平,邓兆卉.分配公平性的分布偏度与峰度描述研究 [J].统计与决策,2008(3):144-147
[3] 余婧.均值-方差-近似偏度投资组合模型和实证分析 [J].运筹学学报,2010,14(1):106-114.
[4] 傅俊辉,张卫国,陆倩,等.考虑偏度风险和峰度风险的非线性期货套期保值模型 [J].系统工程,2009,27(10):44-48.
[5] 王鹏,王建琼,魏宇.自回归条件方差-偏度-峰度:一个新的模型 [J].管理科学学报,2009,12(5):121-129.
[6] Conrad J,Dittmar R F,Ghysels E.Ex ante skewness and expected stock returns [J].The Journal of Finance,2013,68(1):85-124.
[7] Grigoletto M,Lisi F.Looking for skewness in financial time series [J].The Econometrics Journal,2009,12(2):310-323.
[8] Yevjevich V,Obeysekera J T B.Estimation of skewness of hydrologic variables [J].Water Resources Research,1984,20(7):935-943.
[9] Huang Y,Getachew.A Bayesian approach to joint mixed-effects models with a skew-normal distribution and measurement errors in covariates [J].Biometrics,2011,67(1):260-269.
[10] Cabras S,Racugno W,Castellanos M E,et al.A matching prior for the shape parameter of the skew-normal distribution [J].Scandinavian Journal of Statistics,2012,39(2):236-247.
[11] 温利民,邹思思,吕凤虎.偏度系数和峰度系数的信度估计 [J].统计与决策,2015(3):24-25.
[12] Buhlmann H,Gisler A.A course in credibility theory and its applications [M].Netherlands:Springer,2005.
[13] 郑丹,章溢,温利民.具有时间变化效应的信度模型 [J].江西师范大学学报:自然科学版,2012,36(3):249-252.
[14] 方婧,章溢,温利民.聚合风险模型下的信度估计 [J].江西师范大学学报:自然科学版,2012,36(6):607-611.
[15] Robbins H.An empirical Bayes approach to statistics [C]∥Proceedings of the Third Berkeley Symposium on Mathematics,Statistics and Probability,1956:157-164.
[16] Robbins H.The empirical Bayes approach to statistical decision problems [J].Annals of Mathematics Statistics,1964,35(1):1-20.
[17] 李乃医.随机删失下伽玛分布族参数的经验Bayes双边检验 [J].系统科学与数学,2011,31(4):458-465.
[18] Ferguson T S.A course in large-sample theory [M].New York:Chapman and Hall,1996.
[19] Efron B,Tibshirani R.An introduction to the bootstrap [M].New York:Chapman and Hall,1993.

备注/Memo

备注/Memo:
收稿日期:2016-02-19基金项目:国家自然科学基金(71361015),教育部人文社会科学基金(15YJC910010)和江西师范大学研究生创新基金(2014010654)资助项目.作者简介:章 溢(1985-),女,江西南昌人,讲师,主要从事统计学与精算学方面的研究.
更新日期/Last Update: 1900-01-01