偏正态数据下联合位置与尺度模型的统计诊断
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摘要
本文研究偏正态数据下联合位置与尺度模型,考虑基于数据删除模型的参数估计和统计诊断,比较删除模型与未删除模型相应统计量之间的差异.首次提出基于联合位置与尺度模型的诊断统计量和局部影响分析.通过模拟研究和实例分析,给出不同的诊断统计量来判别异常点或强影响点,研究结果表明本文提出的理论和方法是有用和有效的.
In this paper, the joint location and scale models with skew-normal data are investigated.Parameter estimation and statistical diagnostic for case-deletion model are considered, the difference between the corresponding statistics of the model and the non-deleted model is compared. The diagnostic statistics and local influence analysis based on the joint location and scale model are proposed for the first time. Through the simulation and practice, the different diagnostic statistics to identify abnormal point or strong influence point are given, the results show that the proposed theory and method are useful and effective.
In this paper, the joint location and scale models with skew-normal data are investigated.Parameter estimation and statistical diagnostic for case-deletion model are considered, the difference between the corresponding statistics of the model and the non-deleted model is compared. The diagnostic statistics and local influence analysis based on the joint location and scale model are proposed for the first time. Through the simulation and practice, the different diagnostic statistics to identify abnormal point or strong influence point are given, the results show that the proposed theory and method are useful and effective.
引文
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[2]PARK R E.Estimation with heteroscedastic error terms[J].Econometrica,1996,34(4):888.
[3]AITKIN M.Modelling variance heterogeneity in normal regression using GLLM[J].Applied Statistic,1987,36(3):332-339.
[4]马婷,吴刘仓,黄丽.基于偏正态分布联合位置、尺度与偏度模型的极大似然估计[J].数理统计与管理,2013,32(3):433-439.
[5]WU L C,ZHANG Z Z,XU D K.Variable selection in joint location and scale models of the skewnormal distribution[J].Journal of Statistical Computation and Simulation,2013,83(7):1266-1278.
[6]PAULA G A.On diagnostics in double generalized linear models[J].Computational Statistics and Data Analysis,2013,68(68):44-51.
[7]COOK R D,WEISBERG S.Diagnostics for heteroscedasticity in regression[J].Biometrika,1983,70(1):1-10.
[8]XIE F C,LIN J G,WEI B C.Diagnostics for skew-normal nonlinear regression models with AR(1)errors[J].Computational Statistics and Data Analysis,2009,53(12):4403-4416.
[9]VERBYLA A P.Modelling variance heterogeneity:residual maximum likelihood and diagnostics[J].Journal of the Royal Statistical Society,1993,55(2):493-508.
[10]韦博成.参数统计教程[M].北京:高等教育出版社,2006.
[11]韦博成,林金官,解锋昌.统计诊断[M].北京:高等教育出版社,2009.
[12]高惠璇.实用统计方法与SAS系统[M].北京:北京大学出版社,2001.
[2]PARK R E.Estimation with heteroscedastic error terms[J].Econometrica,1996,34(4):888.
[3]AITKIN M.Modelling variance heterogeneity in normal regression using GLLM[J].Applied Statistic,1987,36(3):332-339.
[4]马婷,吴刘仓,黄丽.基于偏正态分布联合位置、尺度与偏度模型的极大似然估计[J].数理统计与管理,2013,32(3):433-439.
[5]WU L C,ZHANG Z Z,XU D K.Variable selection in joint location and scale models of the skewnormal distribution[J].Journal of Statistical Computation and Simulation,2013,83(7):1266-1278.
[6]PAULA G A.On diagnostics in double generalized linear models[J].Computational Statistics and Data Analysis,2013,68(68):44-51.
[7]COOK R D,WEISBERG S.Diagnostics for heteroscedasticity in regression[J].Biometrika,1983,70(1):1-10.
[8]XIE F C,LIN J G,WEI B C.Diagnostics for skew-normal nonlinear regression models with AR(1)errors[J].Computational Statistics and Data Analysis,2009,53(12):4403-4416.
[9]VERBYLA A P.Modelling variance heterogeneity:residual maximum likelihood and diagnostics[J].Journal of the Royal Statistical Society,1993,55(2):493-508.
[10]韦博成.参数统计教程[M].北京:高等教育出版社,2006.
[11]韦博成,林金官,解锋昌.统计诊断[M].北京:高等教育出版社,2009.
[12]高惠璇.实用统计方法与SAS系统[M].北京:北京大学出版社,2001.