单指标众数模型的统计诊断及在波士顿房价分析中的应用
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摘要
在金融、经济、社会科学、气候科学、环境科学、工程技术和生物医学等领域,数据分布常常呈现出尖峰厚尾的特征,且密度分布是不对称的有偏分布。此时,单指标众数模型是刻画这些特征的一个重要方法。为此,非常有必要研究该模型下的统计诊断。本文将考虑单指标众数模型基于数据删除模型和众数漂移模型的统计诊断与局部影响分析。模拟研究和波士顿房价数据的结果表明所提出的方法是有效和可行的。
In the financial, economic, social science, climate science, environmental science, engineering and biomedical sciences, data distribution often shows the characteristics of higher peak and fat tail, and the density distribution is asymmetric distribution of biased. At this case, the single index modal model is an important way to describe these features. Thus, it is very necessary to research statistical diagnosis of the model. In this paper, we are going to investigate the statistical diagnosis of the single index modal model based on data deleted model and mode drift model, and local influence analysis. The simulation studies and a real example about a famous Boston housing data are conducted to illustrate the finite sample performance of the proposed method. The results show that this method is useful and effective.
In the financial, economic, social science, climate science, environmental science, engineering and biomedical sciences, data distribution often shows the characteristics of higher peak and fat tail, and the density distribution is asymmetric distribution of biased. At this case, the single index modal model is an important way to describe these features. Thus, it is very necessary to research statistical diagnosis of the model. In this paper, we are going to investigate the statistical diagnosis of the single index modal model based on data deleted model and mode drift model, and local influence analysis. The simulation studies and a real example about a famous Boston housing data are conducted to illustrate the finite sample performance of the proposed method. The results show that this method is useful and effective.
引文
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[6]Zhu H,Lv Z,Yu K,Deng C.Robust variable selection in partially varying coefficient single-index model[J].Journal of the Korean Statistical Society,2015,44(1):45-57.
[7]Zhao W,Zhang R,Liu J,Lv Y.Robust and efficient variable selection for semiparametric partially linear varying coefficient model based on modal regression[J].Annals of the Institute of Statistical Mathematics,2014,66(1):165-191.
[8]Yang H,Guo C,Lv J.A robust and efficient estimation method for single-index varying-coefficient models[J].Statistics&Probability Letters,2014,94:119-127.
[9]薛留根.单指标模型的统计推断(I)[J]·数理统计与管理,2012,31(2):55-78.
[10]张敏珏,冯予.基于经验似然的AR(p)模型的统计诊断[J]·数理统计与管理,2014,33(2):286-295.
[11]晏振,戴晓文,田茂再·基于杠杆值大数据集抽样的异常点诊断[J].数理统计与管理,2016,35(5):794-802.
[12]韦博成,林金官,解锋昌.统计诊断[M].北京:高等教育出版社,2009.
[13]Hardle W,Hall P,Ichimura H.Optimal smoothing in single-index models[J].The Annals of Statistics,1993,21:157-178.
[14]Xia Y,Tong H,Li W,Zhu L.An adaptive estimation of dimension reduction space[J].Journal of the Royal Statistical society(Series B),2002,64:363-410.
[15]Cook R D,Weisberg S.Residuals and Influence in Regression[M].New York:Chapman and Hall,1982.
[16]Carroll R,Fan J,Gijbels I,Wand M.Generalized partially linear single-index models[J].Journal of the American Statistical Association,1997,92:477-489.
[3]邹清明.单指标模型的几个统计推断问题的研究[D].华东师范大学,2008.
[4]Liu J,Zhao W,Zhang R,Lv Y.A robust and efficient estimation method for the single-index models[J].Multivariate Annals,2013,122:1-27.
[5]Yang H,Yang J.A robust and efficient estimation and variable selection method for A robust and efficient estimation method for single-index varying-coefficient models partially linear single-index models[J].Journal of Multivariate Analysis,2014,129:227-242.
[6]Zhu H,Lv Z,Yu K,Deng C.Robust variable selection in partially varying coefficient single-index model[J].Journal of the Korean Statistical Society,2015,44(1):45-57.
[7]Zhao W,Zhang R,Liu J,Lv Y.Robust and efficient variable selection for semiparametric partially linear varying coefficient model based on modal regression[J].Annals of the Institute of Statistical Mathematics,2014,66(1):165-191.
[8]Yang H,Guo C,Lv J.A robust and efficient estimation method for single-index varying-coefficient models[J].Statistics&Probability Letters,2014,94:119-127.
[9]薛留根.单指标模型的统计推断(I)[J]·数理统计与管理,2012,31(2):55-78.
[10]张敏珏,冯予.基于经验似然的AR(p)模型的统计诊断[J]·数理统计与管理,2014,33(2):286-295.
[11]晏振,戴晓文,田茂再·基于杠杆值大数据集抽样的异常点诊断[J].数理统计与管理,2016,35(5):794-802.
[12]韦博成,林金官,解锋昌.统计诊断[M].北京:高等教育出版社,2009.
[13]Hardle W,Hall P,Ichimura H.Optimal smoothing in single-index models[J].The Annals of Statistics,1993,21:157-178.
[14]Xia Y,Tong H,Li W,Zhu L.An adaptive estimation of dimension reduction space[J].Journal of the Royal Statistical society(Series B),2002,64:363-410.
[15]Cook R D,Weisberg S.Residuals and Influence in Regression[M].New York:Chapman and Hall,1982.
[16]Carroll R,Fan J,Gijbels I,Wand M.Generalized partially linear single-index models[J].Journal of the American Statistical Association,1997,92:477-489.