含缺失数据的约束线性模型回归系数的有偏估计
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摘要
线性模型中参数的有偏估计的研究一直是回归分析的热点问题。基于最小二乘法处理病态阵X共线性问题的不足,线性有偏估计是改进最小二乘估计最直接的方法。无约束线性模型中参数的有偏估计理论的发展已经相对成熟,但在大量的统计问题,如试验设计、方差分析模型和协方差分析模型中,由于附加信息等原因,回归参数满足某些约束条件,这使得带线性等式约束的回归分析具有很重要的研究意义和应用价值。经研究发现,现今通用的一般带约束最小二乘估计同最小二乘估计一样,在处理共线性问题上也存在不足。因此近年来,很多学者试图找更好的方法来改进一般带约束的最小二乘估计方法。
本文试图寻找带约束线性模型中优于最小二乘估计的约束型有偏估计方法,对约束线性回归模型提出了一种新的参数估计的标准(平均散布误差准则),得到了回归系数一种新的约束型有偏估计——条件部分根方估计(CPRSE),并在缺失数据情形下加以应用,探讨了缺失模型(4.2)回归系数的约束型岭估计(RRE)的性质。
第一章综述了目前国内外线性模型参数有偏估计的发展历史和研究现状。
第二章给出了一些预备知识。
第三章在郭建锋及史建红的基础上作者提出了一种新的可容许估计——条件部分根方估计(CPRSE),证明了存在参数k,可使回归系数β的CPRSE的均方误差(MSE)小于约束最小二乘估计(RLSE)的均方误差;在平均散布误差(MDE)准则下给出了CPRSE优于RLSE的充要条件或充分条件;讨论了确定最优尼值的方法。
第四章研究了含缺失数据的约束线性模型,研究了缺失数据的填充法,并进一步对含缺失数据的约束线性模型回归系数建立了条件部分根方估计。
第五章给出了缺失模型(4.2)回归系数β的约束型岭估计(RRE),适当地选择参数k,可使回归系数β的约束型岭估计(RRE)的均方误差(MSE)小于约束最小二乘估计(RLSE)的均方误差;在平均散布误差(MDE)准则下给出了RRE优于RLSE的充要条件或充分条件。
The research of the biased estimation of parameters in the linear model is all the time one of the most popular issues of regression analysis.While dealing with the multicollinearity of design matrix X,the ordinary least squares estimation is always helpless.The linear biased estimation is the most direct method in ameliorating the ordinary least squares estimation.The development of the biased estimation theory of parameters has been relatively mature in the linear regression model without additional restrictions.In a great deal of statistical problems such as in the experiment design,the models of the variance analysis and the covariance analysis and so on,because of additional information and other reasons,regression parameters meet certain restrictive conditions, which show in practice the investigative significances and the applied values of the restricted linear regression.Like the ordinary least squares estimation,the widely applied ordinary restricted least squares estimation is also disadvantageous for dealing with the multicollinearity of design matrix.As a result,a great many researchers recently try to find out better methods to improve the ordinary restricted least squares estimation.
In this dissertation,wetry to seek some biased estimations better than the ordinary restricted least squares estimation in restricted linear regression model.Besides,present a new standard(MDE) for estimating the regression coefficient of restricted linear regression model,and give a new restricted biased estimation of regression coefficient——conditional partial root squares estimation and it is introduced into restricted linear regression model with missing data,and investigate the features of the restricted ridge estimation of regression coefficient in model(4.2) with missing data.
In chapter 1,we discuss the history of development and the current situation of the biased estimation in the linear regression model.
In chapter 2,we give some pre-knowledge.
In chapter 3,on the basis of Guo Jian-Feng and Shi Jian-hong,the author give a new permissible estimation——Conditional partial root squares estimation(CPRSE),prove the existence of parameters k of making mean squares error(MSE) of the Conditional partial root squares estimation less than that of the restricted least squares estimation(RLSE). We gain a necessary and sufficient condition or sufficient conditions which CPRSE is superior to RLSE under the mean dispersion error(MDE) matrix comparisons criterion;and some of methods are discussed to evaluate the optimal value of k.
In chapter 4,we research the restricted linear regression model with missing data and imputation methods in missing data,and we have access to conditional partial root squares estimation(CPRSE) of regression coefficient in restricted Linear regression model with missing data.
In chapter 5,we give the restricted ridge estimation of regression coefficientβin model(4.2) with missing data and k can be chosen to make mean squares error(MSE) of the restricted ridge estimation(RRE) less than of the restricted least squares estimation(RLSE),we gain a necessary and sufficient condition or sufficient conditions which' RRE is superior to RLSE under the mean dispersion error(MDE) matrix comparisons criterion.
本文试图寻找带约束线性模型中优于最小二乘估计的约束型有偏估计方法,对约束线性回归模型提出了一种新的参数估计的标准(平均散布误差准则),得到了回归系数一种新的约束型有偏估计——条件部分根方估计(CPRSE),并在缺失数据情形下加以应用,探讨了缺失模型(4.2)回归系数的约束型岭估计(RRE)的性质。
第一章综述了目前国内外线性模型参数有偏估计的发展历史和研究现状。
第二章给出了一些预备知识。
第三章在郭建锋及史建红的基础上作者提出了一种新的可容许估计——条件部分根方估计(CPRSE),证明了存在参数k,可使回归系数β的CPRSE的均方误差(MSE)小于约束最小二乘估计(RLSE)的均方误差;在平均散布误差(MDE)准则下给出了CPRSE优于RLSE的充要条件或充分条件;讨论了确定最优尼值的方法。
第四章研究了含缺失数据的约束线性模型,研究了缺失数据的填充法,并进一步对含缺失数据的约束线性模型回归系数建立了条件部分根方估计。
第五章给出了缺失模型(4.2)回归系数β的约束型岭估计(RRE),适当地选择参数k,可使回归系数β的约束型岭估计(RRE)的均方误差(MSE)小于约束最小二乘估计(RLSE)的均方误差;在平均散布误差(MDE)准则下给出了RRE优于RLSE的充要条件或充分条件。
The research of the biased estimation of parameters in the linear model is all the time one of the most popular issues of regression analysis.While dealing with the multicollinearity of design matrix X,the ordinary least squares estimation is always helpless.The linear biased estimation is the most direct method in ameliorating the ordinary least squares estimation.The development of the biased estimation theory of parameters has been relatively mature in the linear regression model without additional restrictions.In a great deal of statistical problems such as in the experiment design,the models of the variance analysis and the covariance analysis and so on,because of additional information and other reasons,regression parameters meet certain restrictive conditions, which show in practice the investigative significances and the applied values of the restricted linear regression.Like the ordinary least squares estimation,the widely applied ordinary restricted least squares estimation is also disadvantageous for dealing with the multicollinearity of design matrix.As a result,a great many researchers recently try to find out better methods to improve the ordinary restricted least squares estimation.
In this dissertation,wetry to seek some biased estimations better than the ordinary restricted least squares estimation in restricted linear regression model.Besides,present a new standard(MDE) for estimating the regression coefficient of restricted linear regression model,and give a new restricted biased estimation of regression coefficient——conditional partial root squares estimation and it is introduced into restricted linear regression model with missing data,and investigate the features of the restricted ridge estimation of regression coefficient in model(4.2) with missing data.
In chapter 1,we discuss the history of development and the current situation of the biased estimation in the linear regression model.
In chapter 2,we give some pre-knowledge.
In chapter 3,on the basis of Guo Jian-Feng and Shi Jian-hong,the author give a new permissible estimation——Conditional partial root squares estimation(CPRSE),prove the existence of parameters k of making mean squares error(MSE) of the Conditional partial root squares estimation less than that of the restricted least squares estimation(RLSE). We gain a necessary and sufficient condition or sufficient conditions which CPRSE is superior to RLSE under the mean dispersion error(MDE) matrix comparisons criterion;and some of methods are discussed to evaluate the optimal value of k.
In chapter 4,we research the restricted linear regression model with missing data and imputation methods in missing data,and we have access to conditional partial root squares estimation(CPRSE) of regression coefficient in restricted Linear regression model with missing data.
In chapter 5,we give the restricted ridge estimation of regression coefficientβin model(4.2) with missing data and k can be chosen to make mean squares error(MSE) of the restricted ridge estimation(RRE) less than of the restricted least squares estimation(RLSE),we gain a necessary and sufficient condition or sufficient conditions which' RRE is superior to RLSE under the mean dispersion error(MDE) matrix comparisons criterion.
引文
[1]王松桂,史建红,尹素菊,吴密霞.线性模型引论.科学出版社.2004.
[2]王松桂.线性模型的理论及应用.合肥.安徽教育出版社.1987.
[3]C.Radhakrishna.Rao,Helge Toutenburg.Linear Models[M].Springer-Verlag,1998.
[4]张金槐.线性模型参数估计及其改进[M].长沙:国防科技大学出版社,1999.
[5]田丽娜,王志林.线性回归模型中最小二乘估计的几个结论[J].甘肃高等师范学报,2005,5:13-16
[6]H.Dygas.Week and strong consistency of the least squares estinate in regression model[J].Z/Wahrsch.Verw.Gebiete,34(1976),119-127.
[7]杨复兴.独立误差下线性回归最小二乘相合性的必要条件[J]数学年刊,25(A):2(2004),163-168.
[8]Eicher,F.Asymptotic normality and consistency of the least squares estimates for families of linear regression[J].Ann.Math.Statist,34(1963),447-463.
[9]陈希儒.低阶矩条件下回归最小二乘估计弱相合的充要条件[J].中国科学A辑,25:4(1995),349-358.
[10]Rao,C.R.Linear Statistical Inferenceand Its Application[M].John Wiley,New York,1973.
[11]黄超,肖枝洪,刘贤龙.一个推广增长曲线模型协差阵的最小二乘 估计及其优良性[J].生物数学学报,2004,19(2):226-232.
[12]Rao,C.R.Least squares theory using an estimated dispersion matrix and its application to measurement of signals.In proceedings of the Fifth Berkeley Symposium on Math.Statist &Prob.Eds.by lecan J and Neyman[J].Vol.1.1967:355-361.
[13]Rao,C.R.The Inefficiency of Least squares:Extensions of the Kantorovich inequality.Linear Algebra and its Applications,1985,(70):249-255.
[14]Liski E P,Puntanen S and Wang S G.Bounds for the trace of the difference of the covariance matrices of the OLSE and BLUE [J].Linear Algebra and Its Applications,1992,(172):121-134.
[15]Wang S G and Shao J.Constrained Kantorovich inequalities and relative efficiency of least squares[J].Journal of Multivariate Analysis,1992,(42):284-292.
[16]Wu C F.Characterizing the consistent directions of least squares estimates[J].Ann.statist,1980,8(4):789-796.
[17]Zyskind G.On canonical forms,non-negative covariance mateices and best and simple least squares linear estimator in linear models.Ann.Math.Statist.1967,(38):1092-1100.
[18]王惠文.偏最小二乘回归方法及其应用[M].北京:国防工业出版社,1999:91-141.
[19]茆诗松,王静龙,濮晓龙.高等数理统计[M].北京:高等教育出版 社1998.
[20]夏结来,郭祖超,胡琳.回归系数的根方有偏估计及其应用[J].数理统计与应用概率.1998,1.
[21]刘小茂,张钧.混合系数线性模型参数的根方估计[J].华中理工大学学报,1997,3:111-112.
[22]黄养新.增长曲线模型中回归系数的根方估计[J].工程数学学报,1995,1:61-69
[23]B.Singh,Y.P.Chaubey,T.D.Dwivedi,An almost unbiased ridge estimator,Sankhya:The Indian Journal of Statistics B48(1986)342-346
[24]贾忠贞.回归系数的组合主成分估.数理统计与应用概率.Vol.2no.2(1987)153-158
[25]杨虎.单参数主成分回归估计.高校应用数学学报.1989.1.74-80.
[26]归庆明.多元广义主成分估计类.数理统计与应用概率.1994.3.1-13.
[27]夏结来,郭祖超,胡琳.回归系数的广义根方估计及其模拟[J].应用数学,1994,2.
[28]徐文莉,林举干.岭型组合主成分估计.应用概率统计.1995.2.52-59.
[29]于义良,宋卫星.回归系数的根方型主成分估计.山西师大学报(自然科学版:英文)1995.9.14-19.
[30]于义良,宋卫星.回归系数的stein型主成分估计.数学研究.1995,9.85-88.
[31]Yu Yi liang,Song Wei xing.Combing Root and principal components Estimates of Regression coefficient.山西师大学报(自然科学版), 1995.3:15-20.
[32]高兑现,黄养新.多元线性模型回归系数的广义根方估计[J].西安矿业学院学报,1996,3:275-279.
[33]夏正茂,梁家荣.多元线性模型系数的广义根方改进估计类[J].西北大学学报(自然科学版),1996,6:467-471.
[34]林路.回归系数的综合岭估计.数理统计与应用概率.1996.9.179-185.
[35]Aldrin,M.Length Modified Ridge Regression.Computational Statistics and Data Analysis 1997,25,377:398.
[36谆ij建锋,归庆明,张建军.测量平差系统病态性的诊断与处理.中国人民解放军信息工程大学.2002.4.
[37]陈希孺,王松桂.近代回归分析.合肥.安徽教育出版社.1987.
[38]史建红.约束线性回归模型的条件岭型估计[J].山西教育学院学报.1999,3:19-22.
[39]史建红.约束线性回归模型回归系数的条件岭型估计[J].山西师范大学学报,2001,12,15(4):10-16.
[40]史建红.约束线性模型下回归系数的条件根方估计[J].沈阳师范学院学报(自然科学版),1999,4:13-19.
[41]农秀丽,刘万荣.非齐次等式约束线性回归模型的条件根方估计[J].重庆师范大学学报(自然科学版),2007,2:24-28.
[42]Hu Yang,Li-xing Zhu.Adaptive Unified Biased Estimators of Parameters in Linear Model.Acta Mathematicae Applicatae Sinica.vol.20,No.3(2004).425-432.
[43]Sarkar,N.A new estimator combining the ridge regression and the restricted least squares methods of estimation.Comm.Statist.Theory Methods.1992.21.1987-2000.
[44]Jiirgen Groβ.Restricted ridge estimation.Statistics& Probability Letter.2003.65.57-64
[45]Magness T A and McGuire J B.comparison of least squares and minimum variance estimates of regression parameter.Ann.Math.Statist..1962,(33)462-474.
[46]詹金龙,陈建宝.带约束的回归系数的线性估计的可容许性[J].高校应用数学学报,1(1991).
[47]吴启光.矩阵损失下随机回归系数和参数的线性估计的可容许性[J].系统科学和数学,8(1)(1988):1-10.
[48]孙孝前.受约束线性模型中的可容许线性估计[J].贵州师范大学学报(自然科学版),1995,4:43-46.
[49]J Han,M Kamber,Data Mining:Concepts and Techniques,Morgan Kaufmann Publishers,Inc.2001.
[50]E Hung,D W Cheung,Parallel mining of outliers in Large Database,Distributed and Parallel Databases,2002 12(1):5-26.
[51]杨虎,钟震,程代杰.基于不完全数据的异常挖掘算法研究.计算机研究与发展.2004,9.1532-1539.
[52]柏松,杨虎.Pitman优良性以及不完全数据挖掘的进一步研究[D].重庆大学数理学院.2007,4.
[53]朱晓峰,张师超.缺失值填充的若干问题研究[D].广西师大.2004.
[54]张成萍,易昆南.残缺数据的填补[D].中南大学.2006,11.
[55]梁霞,易昆南.缺失数据的多重插补及其改进[D].中南大学.2007,5.
[56]冯志兰,刘桂芬.缺失数据的估计与应用[D].山西医科大学.2003,5.
[57]钟震.线性模型中的约束型有偏估计的研究[D].重庆大学数理学院.2005.10
[58]郑昌光.约束条件下的线性估计[J].应用概率统计,1986,1.
[59]鹿长余.线性模型中参数估计的可容许理论[J].应用概率统计2001(17)2:203-212.
[60]王松桂.线性模型参数估计的新进展[J].数学进展,1985,3:193-204.
[61]张卫国,王利岩,陈炜.带有约束条件的一般线性模型参数估计[J].河北师范大学学报(自然科学版),2004,3:241-244.
[62]张双林.带约束线性模型中的可容许线性估计[J].应用数学学报,1994,3:470-472.
[63]Bloomfield P and Watson G S.The effecency of least squares.Biometrika,1975,(62):162-168.
[64]ROBERT J.SERFLING.Approximation Theorems of Mathematical statist,1978.
[65]杨文礼.线性模型引论[M].北京:北京师范大学出版社,1998.
[2]王松桂.线性模型的理论及应用.合肥.安徽教育出版社.1987.
[3]C.Radhakrishna.Rao,Helge Toutenburg.Linear Models[M].Springer-Verlag,1998.
[4]张金槐.线性模型参数估计及其改进[M].长沙:国防科技大学出版社,1999.
[5]田丽娜,王志林.线性回归模型中最小二乘估计的几个结论[J].甘肃高等师范学报,2005,5:13-16
[6]H.Dygas.Week and strong consistency of the least squares estinate in regression model[J].Z/Wahrsch.Verw.Gebiete,34(1976),119-127.
[7]杨复兴.独立误差下线性回归最小二乘相合性的必要条件[J]数学年刊,25(A):2(2004),163-168.
[8]Eicher,F.Asymptotic normality and consistency of the least squares estimates for families of linear regression[J].Ann.Math.Statist,34(1963),447-463.
[9]陈希儒.低阶矩条件下回归最小二乘估计弱相合的充要条件[J].中国科学A辑,25:4(1995),349-358.
[10]Rao,C.R.Linear Statistical Inferenceand Its Application[M].John Wiley,New York,1973.
[11]黄超,肖枝洪,刘贤龙.一个推广增长曲线模型协差阵的最小二乘 估计及其优良性[J].生物数学学报,2004,19(2):226-232.
[12]Rao,C.R.Least squares theory using an estimated dispersion matrix and its application to measurement of signals.In proceedings of the Fifth Berkeley Symposium on Math.Statist &Prob.Eds.by lecan J and Neyman[J].Vol.1.1967:355-361.
[13]Rao,C.R.The Inefficiency of Least squares:Extensions of the Kantorovich inequality.Linear Algebra and its Applications,1985,(70):249-255.
[14]Liski E P,Puntanen S and Wang S G.Bounds for the trace of the difference of the covariance matrices of the OLSE and BLUE [J].Linear Algebra and Its Applications,1992,(172):121-134.
[15]Wang S G and Shao J.Constrained Kantorovich inequalities and relative efficiency of least squares[J].Journal of Multivariate Analysis,1992,(42):284-292.
[16]Wu C F.Characterizing the consistent directions of least squares estimates[J].Ann.statist,1980,8(4):789-796.
[17]Zyskind G.On canonical forms,non-negative covariance mateices and best and simple least squares linear estimator in linear models.Ann.Math.Statist.1967,(38):1092-1100.
[18]王惠文.偏最小二乘回归方法及其应用[M].北京:国防工业出版社,1999:91-141.
[19]茆诗松,王静龙,濮晓龙.高等数理统计[M].北京:高等教育出版 社1998.
[20]夏结来,郭祖超,胡琳.回归系数的根方有偏估计及其应用[J].数理统计与应用概率.1998,1.
[21]刘小茂,张钧.混合系数线性模型参数的根方估计[J].华中理工大学学报,1997,3:111-112.
[22]黄养新.增长曲线模型中回归系数的根方估计[J].工程数学学报,1995,1:61-69
[23]B.Singh,Y.P.Chaubey,T.D.Dwivedi,An almost unbiased ridge estimator,Sankhya:The Indian Journal of Statistics B48(1986)342-346
[24]贾忠贞.回归系数的组合主成分估.数理统计与应用概率.Vol.2no.2(1987)153-158
[25]杨虎.单参数主成分回归估计.高校应用数学学报.1989.1.74-80.
[26]归庆明.多元广义主成分估计类.数理统计与应用概率.1994.3.1-13.
[27]夏结来,郭祖超,胡琳.回归系数的广义根方估计及其模拟[J].应用数学,1994,2.
[28]徐文莉,林举干.岭型组合主成分估计.应用概率统计.1995.2.52-59.
[29]于义良,宋卫星.回归系数的根方型主成分估计.山西师大学报(自然科学版:英文)1995.9.14-19.
[30]于义良,宋卫星.回归系数的stein型主成分估计.数学研究.1995,9.85-88.
[31]Yu Yi liang,Song Wei xing.Combing Root and principal components Estimates of Regression coefficient.山西师大学报(自然科学版), 1995.3:15-20.
[32]高兑现,黄养新.多元线性模型回归系数的广义根方估计[J].西安矿业学院学报,1996,3:275-279.
[33]夏正茂,梁家荣.多元线性模型系数的广义根方改进估计类[J].西北大学学报(自然科学版),1996,6:467-471.
[34]林路.回归系数的综合岭估计.数理统计与应用概率.1996.9.179-185.
[35]Aldrin,M.Length Modified Ridge Regression.Computational Statistics and Data Analysis 1997,25,377:398.
[36谆ij建锋,归庆明,张建军.测量平差系统病态性的诊断与处理.中国人民解放军信息工程大学.2002.4.
[37]陈希孺,王松桂.近代回归分析.合肥.安徽教育出版社.1987.
[38]史建红.约束线性回归模型的条件岭型估计[J].山西教育学院学报.1999,3:19-22.
[39]史建红.约束线性回归模型回归系数的条件岭型估计[J].山西师范大学学报,2001,12,15(4):10-16.
[40]史建红.约束线性模型下回归系数的条件根方估计[J].沈阳师范学院学报(自然科学版),1999,4:13-19.
[41]农秀丽,刘万荣.非齐次等式约束线性回归模型的条件根方估计[J].重庆师范大学学报(自然科学版),2007,2:24-28.
[42]Hu Yang,Li-xing Zhu.Adaptive Unified Biased Estimators of Parameters in Linear Model.Acta Mathematicae Applicatae Sinica.vol.20,No.3(2004).425-432.
[43]Sarkar,N.A new estimator combining the ridge regression and the restricted least squares methods of estimation.Comm.Statist.Theory Methods.1992.21.1987-2000.
[44]Jiirgen Groβ.Restricted ridge estimation.Statistics& Probability Letter.2003.65.57-64
[45]Magness T A and McGuire J B.comparison of least squares and minimum variance estimates of regression parameter.Ann.Math.Statist..1962,(33)462-474.
[46]詹金龙,陈建宝.带约束的回归系数的线性估计的可容许性[J].高校应用数学学报,1(1991).
[47]吴启光.矩阵损失下随机回归系数和参数的线性估计的可容许性[J].系统科学和数学,8(1)(1988):1-10.
[48]孙孝前.受约束线性模型中的可容许线性估计[J].贵州师范大学学报(自然科学版),1995,4:43-46.
[49]J Han,M Kamber,Data Mining:Concepts and Techniques,Morgan Kaufmann Publishers,Inc.2001.
[50]E Hung,D W Cheung,Parallel mining of outliers in Large Database,Distributed and Parallel Databases,2002 12(1):5-26.
[51]杨虎,钟震,程代杰.基于不完全数据的异常挖掘算法研究.计算机研究与发展.2004,9.1532-1539.
[52]柏松,杨虎.Pitman优良性以及不完全数据挖掘的进一步研究[D].重庆大学数理学院.2007,4.
[53]朱晓峰,张师超.缺失值填充的若干问题研究[D].广西师大.2004.
[54]张成萍,易昆南.残缺数据的填补[D].中南大学.2006,11.
[55]梁霞,易昆南.缺失数据的多重插补及其改进[D].中南大学.2007,5.
[56]冯志兰,刘桂芬.缺失数据的估计与应用[D].山西医科大学.2003,5.
[57]钟震.线性模型中的约束型有偏估计的研究[D].重庆大学数理学院.2005.10
[58]郑昌光.约束条件下的线性估计[J].应用概率统计,1986,1.
[59]鹿长余.线性模型中参数估计的可容许理论[J].应用概率统计2001(17)2:203-212.
[60]王松桂.线性模型参数估计的新进展[J].数学进展,1985,3:193-204.
[61]张卫国,王利岩,陈炜.带有约束条件的一般线性模型参数估计[J].河北师范大学学报(自然科学版),2004,3:241-244.
[62]张双林.带约束线性模型中的可容许线性估计[J].应用数学学报,1994,3:470-472.
[63]Bloomfield P and Watson G S.The effecency of least squares.Biometrika,1975,(62):162-168.
[64]ROBERT J.SERFLING.Approximation Theorems of Mathematical statist,1978.
[65]杨文礼.线性模型引论[M].北京:北京师范大学出版社,1998.
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