[1]李小雪,明瑞星.高维协方差矩阵估计方法的比较[J].江西师范大学学报(自然科学版),2015,(06):599-604.
 LI Xiaoxue,MING Ruixing.The Comparison of Methods for Estimating the High-Dimensional Covariance Matrices[J].Journal of Jiangxi Normal University:Natural Science Edition,2015,(06):599-604.
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高维协方差矩阵估计方法的比较()
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《江西师范大学学报》(自然科学版)[ISSN:1006-6977/CN:61-1281/TN]

卷:
期数:
2015年06期
页码:
599-604
栏目:
出版日期:
2015-12-31

文章信息/Info

Title:
The Comparison of Methods for Estimating the High-Dimensional Covariance Matrices
作者:
李小雪;明瑞星
浙江工商大学统计与数学学院,浙江 杭州 310018
Author(s):
LI XiaoxueMING Ruixing
School of Statistics and Mathematics,Zhejiang Gongshang University,Hangzhou Zhejiang 310018,China
关键词:
高维协方差矩阵 稀疏矩阵 非稀疏矩阵 门限估计 收缩估计
Keywords:
high-dimensional covariance matrix sparse matrix non-parse matrix thresholding estimation shrinkage estimation
分类号:
F 224
文献标志码:
A
摘要:
通过模拟比较门限估计方法和收缩估计方法之间的差异,得出2种方法在实际应用中的使用范围.由模拟结果可知,若有确切的证据表明总体协方差矩阵是稀疏矩阵,则采用门限估计方法,否则,采用稳健的收缩估计方法比较恰当.
Abstract:
The differences between the thresholding estimation and the shrinking estimation are reported by a series of simulations,and the proper estimation is proposed within these two estimations in practice.The simulations show that if the population covariance matrix is a sparse matrix,the thresholding estimation is better than that of the shrinking estimation,and vice versa.

参考文献/References:

[1] Anderson T W.An introduction to multivariate statistical analysis [M].3rd ed.New York:John Wiley and Sons,2003.
[2] 白志东,郑术蓉,姜丹丹.大维统计分析 [M].北京:高等教育出版社,2012.
[3] Schafer J,Strimmer K.A shrinkage approach to large-scale covariance matrix estimation and implications for functional genomics [J].Statistical Applications in Genetics and Molecular Biology,2005,4(1):1-32.
[4] Bickel P J,Levina E.Covariance regularization by thresholding [J].Annals of Statistics,2008,36(6): 2577-2604.
[5] Rothman A J,Levina,E,Zhu Ji.Generalized thresholding of large covariance matrices [J].Journal of the American Statistical Association,2009,104(485):177-186.
[6] Cai Tony T,Zhang Cunhui,Zhou Harrison H.Optimal rates of convergence for covariance matrix estimation [J].Annals of Statistics,2010,38(4):2118-2144.
[7] Fan Jianqing,Liao Yuan,Mincheva M.High dimensional covariance matrix estimation in approximate factor models [J].Annals of Statistics,2011,39(6): 3320-3356.
[8] Fan Jianqing,Liao Yuan,Mincheva M.Large covariance estimation by thresholding principal orthogonal complements [J].Journal of the Royal Statistical Society,2011,75(4): 603-680.
[9] Furrer R,Bengtsson T.Estimation of high-dimensional prior and posterior covariance matrices in Kalman filter varaiants [J].Journal of Multivariate Analysis,2007,98(2): 227-255.
[10] Bickel P J,Levina E.Regularized estimation of large covariance matrices [J].Annals of Statistics,2008,36(1): 199-227.
[11] Wu Weibiao,Pourahmadi M.Banding sample autocovariance matrices of stationary processes [J].Statistica Sinica,2009,19(4): 1755-1768.
[12] Cai Tony T,Liu Weidong.Adaptive thresholding for sparse covariance matrixestimation [J].Journal of the American Statistical Association,2011,106(494): 672-684.
[13] Rothman A J,Levina E,Zhu Ji.A new approach to cholesky-based covariance regularization in high dimensions [J].Biometrika,2010,97(3): 539-550.
[14] Anderes E,Huser R,Nychka D,et al.Nonstationary positive definite tapering on the plane [J].Journal of Computational and Graphical Statistics,2013,22(4): 848-865.
[15] Stein M L.Statistical properties of covariance tapers [J].Journal of Computational and Graphical Statistics,2013,22(4): 866-885.
[16] Bickel P J,Levina E.Some theory for Fisher's linear discriminant function,“naive Bayes,” and some alternatives when there are many more variables than observations [J].Bernoulli,2004,10(6): 989-1010.
[17] Qiu Yumou,Chen Songxi.Test for bandedness of high-dimensional covariance matrices and bandwidth estimation [J].Annals of Statistics,2012,40(3): 1285-1314.
[18] Qiu Yumou,Chen Songxi.Band width selection for high dimensional covariance estimation [J].Journal of the American Statistical Association,2014,119(1):1-35.
[19] Yi Feng,Zou Hui.Sure-tuned tapering estimation of large covariance matrices [J].Computational Statistics and Data Analysis,2013,58(1): 339-351.
[20] Bien J,Bunea F,Xiao Luo.Convex banding of the covariance matrix [J].Journal of the American Statistical Association,2014,doi:10.1080/01621459.2015.1058265.
[21] Fan Jianqing,Fan Yingying,Lv Jinchi.High dimensional covariance matrix estimation using a factor model [J].Journal of Econometrics,2008,147(1): 186-197.
[22] Stein C.Inadmissibility of the usual estimator for the mean of a multivariate normal distribution [J].Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability,1956,1:197-206.
[23] Ledoit O,Wolf M.A well-conditioned estimator for large-dimensional covariance matrices [J].Journal of Multivariate Analysis,2004,88(2): 365-411.

备注/Memo

备注/Memo:
基金项目:浙江省高校人文社科重点研究基地(统计学),浙江省自然科学基金(LY16A01001)和浙江省教育厅课题(1020KZ0413455)资助项目.
更新日期/Last Update: 1900-01-01