JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2015, Vol. 50 ›› Issue (06): 33-38.doi: 10.6040/j.issn.1671-9352.0.2014.201

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Minimax estimator for multivariate linear model of regression coefficient matrix

GAO Ting-ting, FAN Guo-liang   

  1. School of Math-Physics, Anhui Polytechnic University, Wuhu 241000, Anhui, China
  • Received:2014-05-06 Revised:2015-01-06 Online:2015-06-20 Published:2015-07-31

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Abstract: For the multivariate linear model Y=XΘ+ε, E(ε)=0, COV(ε)=σ2▽⊗Σ, where ▽>0 and Σ≥0 are known matrix, the minimax estimator of regression coefficients matrix in the multivariate linear model was considered. Under the matrix loss function, the property of linear estimators was investigated. The unique minimax estimator of linearly estimable functions SΘ of coefficients matrix was obtained under the suitable hypotheses.

Key words: Minimax estimator, regression coefficients matrix, matrix loss

CLC Number: 

  • O212
[1] 徐兴忠.矩阵损失下回归系数的线性Minimax估计[J].系统科学与数学,1990,10(4):296-300. XU Xingzhong. The linear Minimax estimate of regression coefficient under matrix loss function[J]. Sys Sci & Math Scis, 1990, 10(4):296-300.
[2] 徐兴忠.二次损失下回归系数的线性Minimax估计[J].数学年刊,1993,14A(5):621-628. XU Xingzhong. The linear Minimax estimate of regression coefficient under quadratic loss function[J]. Chinese Annals of Mathematics Series, 1993, 14A(5):621-628.
[3] 喻胜华.二次损失下一般Gauss-Markov模型中可估函数的线性Minimax估计[J].应用数学学报, 2003,26(4):693-701. YU Shenghua. The linear Minimax estimators of estimable function in a general Gauss-Markov model under quadratic loss function[J]. Acta Mathematicae Applicatae Sinica, 2003, 26(4):693-701.
[4] 陈清平,谢民育.矩阵损失下多元回归系数线性估计的Minimax可容许性的特征[J].系统科学与数学,1995,15(1):24-29. CHEN Qingping, XIE Minyu. The Minimax admissibility characterization of linear estimates of multivariate regression coefficient under matrix loss function[J]. Sys Sci & Math Scis, 1995, 15(1):24-29.
[5] 赵建昕,翟延慧, 齐毅.增长曲线模型中回归系数的线性Minimax估计[J].吉林大学学报:自然科学版,2001,2:5-9. ZHAO Jianxin, ZHAI Yanhui, QI Yi. The linear Minimax estimation of regression coefficients in growth curve model[J]. Acta Scientiarum Journal Social Science, 2001, 2:5-9.
[6] 徐礼文,王松桂.二次损失下随机回归系数和参数的线性Minimax估计[J].数学年刊,2005,26A(5):683-694. XU Liwen, WANG Songgui. The linear Minimax estimator of stochastic regression coefficients and parameters under quadratic loss funtion[J]. Chinese Annals of Mathematics Series, 2005, 26A(5):683-694.
[7] 徐礼文,陆璇,王松桂.矩阵损失下线性混合模型中的局部线性Minimax估计[J].工程数学学报,2008,25(5):851-856. XU Liwen, LU Xuan, WANG Songgui. The local linear Minimax estimator for linear mixed models under matrix loss[J]. Chinese Journal of Engineering Mathematics, 2008, 25(5):851-856.
[8] 吴雄韬,易艳春.二次损失下G-M模型中可估函数的条件Minimax估计与性质[J].大学数学, 2012,28(5):86-89. WU Xiongtao, YI Yanchun. Under the quadratic funtion limited Minimax estimator of the estimated function in the G-M model[J]. College Mathematics, 2012, 28(5):86-89.
[9] 杜广富,贺瑞缠.LINEX损失函数下位置参数函数的极小极大估计[J].纯粹数学与应用数学, 2011,27(3):383-386. DU Guangfu, HE Ruichan. LINEX loss funtion position parameter function under the minimax estimate[J]. Pure and Applled Mathematics, 2011, 27(3):383-386.
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