偏t正态数据下混合线性联合位置与尺度模型的参数估计
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摘要
偏t正态分布是分析尖峰,厚尾数据的重要统计工具之一.研究提出了偏t正态数据下混合线性联合位置与尺度模型,通过EM算法和Newton-Raphson方法研究了该模型参数的极大似然估计.并通过随机模拟试验验证了所提出方法的有效性.最后,结合实际数据验证了该模型和方法具有实用性和可行性.
Skew-t-normal distribution is one of the most important statistical tools to analyze the obvious peak and fat tail data. A linear mixture joint location and scale model with skew-t-normal data is proposed in this paper. The maximum likelihood estimation of the unknown parameters of this model is investigated based on Expectation Maximization(EM) algorithm and Newton-Raphson method. Furthermore, the proposed procedure works satisfactorily through Monte Carlo experiments.Finally, a real example shows that both this model and method are useful and effective.
Skew-t-normal distribution is one of the most important statistical tools to analyze the obvious peak and fat tail data. A linear mixture joint location and scale model with skew-t-normal data is proposed in this paper. The maximum likelihood estimation of the unknown parameters of this model is investigated based on Expectation Maximization(EM) algorithm and Newton-Raphson method. Furthermore, the proposed procedure works satisfactorily through Monte Carlo experiments.Finally, a real example shows that both this model and method are useful and effective.
引文
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[4]Song Weixing,Yao Wenxin,Xing Yanru.Robust mixture regression models fitting by Laplace distribution[J].Computational Statistics and Data Analysis,2014,71:128-137.
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[9]吴刘仓,马婷,戴琳.基于St N分布下联合位置与尺度模型的极大似然估计[J].应用数学,2013,26:671-676.
[10]Aitkin M.Modelling variance heterogeneity in normal regression using GLIM[J].Applied Statistics,1987,36:332-339.
[11]吴刘仓,张忠占,徐登可.联合均值与方差模型的变量选择[J].系统工程理论与实践,2012,32:1754-1760.
[12]Go′mez H W,Venegas O,Bolfarine H.Skew-symmetric distributions generated by the distribution function of the normal distribution[J].Environmetric,2007,18:395-407.
[13]吴刘仓,张家茂,李玲雪.缺失偏t正态数据下线性回归模型的统计推断[J].应用数学,2015,28:16-25.
[14]Lin Jinguan,Xie Fengchang,Wei Bocheng.Statistical diagnostics for skew-t-normal nonlinear models[J].Communications in Statistics-Simulation and Computation,2009,38:2096-2110.
[15]Taylor and Francis.Finite mixture of generalized semiparametric models variable slection via penalized estimation[J].Communications in Statistics-Simulation and Computation,2015,DOI:10.1080/03610918.2014.953687.
[16]Cook A D,Weisberg S.An introduction to regression graphics[M].John Wiley Sons,1994.
[2]Mc Lachlan G,Peel D.Finite Mixture Models[M].New York:Wiley,2000.
[3]Yao Wenxin,Wei Yan,Yu Chun.Robust mixture regression models using t-distribution[J].Computational Statistics and Data Analysis,2014,71:116-127.
[4]Song Weixing,Yao Wenxin,Xing Yanru.Robust mixture regression models fitting by Laplace distribution[J].Computational Statistics and Data Analysis,2014,71:128-137.
[5]Azzalini A.A class of distributions which includes the normal ones[J].Scandinavian Journal of Statistics,1985,2:171-178.
[6]Kotz S,Vicari D.Survey of developments in the theory of continuous skewed distributions[J].International Journal of Statistics,2005,2:225-261.
[7]Nadarajah S,Kotz S.Skew distributions generated from different families[J].Acta Applicandae Mathematica,2006,91:1-37.
[8]Liu Min,Lin Tsung-I.A skew-normal mixture regression model[J].Educational and Psychological Measurement,2014,74:139-162.
[9]吴刘仓,马婷,戴琳.基于St N分布下联合位置与尺度模型的极大似然估计[J].应用数学,2013,26:671-676.
[10]Aitkin M.Modelling variance heterogeneity in normal regression using GLIM[J].Applied Statistics,1987,36:332-339.
[11]吴刘仓,张忠占,徐登可.联合均值与方差模型的变量选择[J].系统工程理论与实践,2012,32:1754-1760.
[12]Go′mez H W,Venegas O,Bolfarine H.Skew-symmetric distributions generated by the distribution function of the normal distribution[J].Environmetric,2007,18:395-407.
[13]吴刘仓,张家茂,李玲雪.缺失偏t正态数据下线性回归模型的统计推断[J].应用数学,2015,28:16-25.
[14]Lin Jinguan,Xie Fengchang,Wei Bocheng.Statistical diagnostics for skew-t-normal nonlinear models[J].Communications in Statistics-Simulation and Computation,2009,38:2096-2110.
[15]Taylor and Francis.Finite mixture of generalized semiparametric models variable slection via penalized estimation[J].Communications in Statistics-Simulation and Computation,2015,DOI:10.1080/03610918.2014.953687.
[16]Cook A D,Weisberg S.An introduction to regression graphics[M].John Wiley Sons,1994.