中国人口预测的半参数模型
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摘要
有关中国人口预测的模型有很多种,传统的线性模型在实际应用中常常存在设定误差,非参数回归模型则是假定变量间的关系未知,对整个回归函数进行估计,能更好的拟合样本数据,并对数据做出较为精确的预测。半参数模型由于融合了非参数模型和线性模型的优点,具有更强的解释能力,而且还较好的避免了“维数祸根”这一问题,受到诸多学者的广泛关注。近年来,半参数模型在人口建模中也有所应用,但是半参数方法的应用主要集中于核类方法,对于全局光滑的样条方法和基于重抽样思想的Bootstrap方法在人口预测中的应用还有待进一步的研究。
本文主要从三个不同的方面建立中国人口预测的半参数回归模型。首先,基于时间序列分析建立线性自回归模型,同时基于多项式样条估计理论建立了半参数自回归模型,将这两种模型分别对中国人口进行拟合与预测对比,结果显示半参数自回归模型优于线性模型;其次,考虑到中国人口与GDP存在着高度的相关性,建立以GDP为外生变量的半参数回归模型,并与以GDP为非参数函数的非参数模型和以GDP为线性主部的半参数模型进行对比,结果显示本文建立的以GDP为非参数函数的的半参数回归模型更优一些;最后,尝试采用Bootstrap方法和多项式样条估计对建立的半参数模型中的参数和非参数函数进行点估计,得到半参数回归方程对中国人口进行拟合及预测,结果表明基于Bootstrap方法的半参数回归模型对中国人口拟合和预测精度均较好。
There are many different prediction models about the total population of China. Setting errors are existed in the practical applications in the traditional linear models, however the whole regression function is estimated and the sample data can be fitted better and predicted accurately in the nonparametric regression models because of assuming the relationships among the variables of the models are unknown. Semi-parametric model has more explanatory power and can avoid the“dimension curse”better with merging the advantages of non-parametric model and linear model, therefore the semi-parametric models are populated by many scholars. In recent years, semi-parametric regressive prediction model has also been applied in the model for population, but the applications of estimation of the semi-parametric model are focuse of kernel methods, spline smoothing method of global methods and Bootstrap method based on the resampling are not found and applied in the population in the literatures.
Semi-parametric regressive prediction model for pupulation of China is done under three main cases. Firsrt, the linear regressive model is done based on theory of time series analysis, and semi-parametric regressive model is estimated based on the theory of spline estimation, then the observations of Chinese population are fitted and predicted using the two models, simulated results show the established semiparametric regression model is superior to some traditional models. Second, a semi-parametric autoregression model with an exogenous variable for population of China is presented considering high correlation between the GDP and chinese population, comparing the prediction results with the non-parametric model with GDP is the non-parmetric funtion and semi-parametric regressive prediction model with GDP is the linear main part of model, the result show that semi-parametric regressive model done in this paper is another better model. Finally, semi-parametric regressive prediction model for pupulation of China is done based on the theory of spline and bootstrap method, semiparametric autoregression model is set up, and the Chinese population are fitted and predicted,the results show that accuracy of fit and prediction of the total population of China are higher.
本文主要从三个不同的方面建立中国人口预测的半参数回归模型。首先,基于时间序列分析建立线性自回归模型,同时基于多项式样条估计理论建立了半参数自回归模型,将这两种模型分别对中国人口进行拟合与预测对比,结果显示半参数自回归模型优于线性模型;其次,考虑到中国人口与GDP存在着高度的相关性,建立以GDP为外生变量的半参数回归模型,并与以GDP为非参数函数的非参数模型和以GDP为线性主部的半参数模型进行对比,结果显示本文建立的以GDP为非参数函数的的半参数回归模型更优一些;最后,尝试采用Bootstrap方法和多项式样条估计对建立的半参数模型中的参数和非参数函数进行点估计,得到半参数回归方程对中国人口进行拟合及预测,结果表明基于Bootstrap方法的半参数回归模型对中国人口拟合和预测精度均较好。
There are many different prediction models about the total population of China. Setting errors are existed in the practical applications in the traditional linear models, however the whole regression function is estimated and the sample data can be fitted better and predicted accurately in the nonparametric regression models because of assuming the relationships among the variables of the models are unknown. Semi-parametric model has more explanatory power and can avoid the“dimension curse”better with merging the advantages of non-parametric model and linear model, therefore the semi-parametric models are populated by many scholars. In recent years, semi-parametric regressive prediction model has also been applied in the model for population, but the applications of estimation of the semi-parametric model are focuse of kernel methods, spline smoothing method of global methods and Bootstrap method based on the resampling are not found and applied in the population in the literatures.
Semi-parametric regressive prediction model for pupulation of China is done under three main cases. Firsrt, the linear regressive model is done based on theory of time series analysis, and semi-parametric regressive model is estimated based on the theory of spline estimation, then the observations of Chinese population are fitted and predicted using the two models, simulated results show the established semiparametric regression model is superior to some traditional models. Second, a semi-parametric autoregression model with an exogenous variable for population of China is presented considering high correlation between the GDP and chinese population, comparing the prediction results with the non-parametric model with GDP is the non-parmetric funtion and semi-parametric regressive prediction model with GDP is the linear main part of model, the result show that semi-parametric regressive model done in this paper is another better model. Finally, semi-parametric regressive prediction model for pupulation of China is done based on the theory of spline and bootstrap method, semiparametric autoregression model is set up, and the Chinese population are fitted and predicted,the results show that accuracy of fit and prediction of the total population of China are higher.
引文
[1]宋健.人口控制[J].自动化学报,1989,15(5):385-391.
[2]宋健,于景元.人口控制论[J].软科学研究,1989,(1):1-7.
[3]龚跃,党宏.人口预测的模型与方法[J].长春光学精密机械学院学报,1991,14(3):83-92.
[4]王伟华,宋宇婷,王福胜等.一类人口发展方程解的存在性和收敛性的研究[J].哈尔滨师范大学自然科学学报,2006,22(2):15-17.
[5]何朗,赵韫,管坤等.人口发展的参数预测模型[J].武汉理工大学学报(信息与管理工程版),2008,30(3):494-497.
[6]邹春松.“人口自然增长率”计算方法亟需改进[J].统计与决策,1991,(4):44-44.
[7]茆长宝,程琳.两种人口预测模型的精确度比较—以人口年龄移算法和灰色预测模型为例[J].南京人口管理干部学院学报,2009,(1):29-32.
[8]谢建文,张元标,王志伟等.基于宋健人口模型的老年化预测[J]. 2008,36(12):5227-5229.
[9]王勇. Logistic人口模型的求解问题[J].哈尔滨商业大学学报(自然科学版),2006,22(5):58-59.
[10]李百岁,同力嘎.内蒙古人口城市化Logistic模型及其应用[J].干旱区资源与环境,2007,21(2):32-36.
[11]冯守平.中国人口增长预测模型[J].安徽科技学院学报,2008,22(6):73-76.
[12]陈文权,赵兹,李得胜. Leslie修正模型在人口预测中的应用[J].世界科技研究与发展,2008,30(2):219-224.
[13] Lee R. D., Tuljapurkar, S. Stochastic Popultation Forecasts for the US Meetings of the Population[J]. Association of Amercia in Washington D.C., 1991.
[14] Lee. R.D. ,Carter L. Modeling and Forecasting US Moratlity[C]. Annual Meetings of the Population Association of America (Toronto),1990.
[15] Pollard.H.. Mathematical Models for the Grouth of Human Population[M].University Press, Cambridge,1975:112-134.
[16]李南,Tuljapurkar S.基于时间一区域序列的随机死亡率预测及对中国数据的应用[J].人口研究,1995,(4):58-63.
[17]李南,申卯兴.基于随机模型的中国生育率预测[J].预测,1996,15(6):33-36.
[18]李南,胡华清.基于随机方法的中国人口预测与规划[J].系统工程理论方法应用,1998,7(1):37-41.
[19]付莹.回归分析在人口预测中的应用[J].辽宁高职学报,2000,2(1):56-58.
[20]李旭东.贵州喀斯特高原人口分布的自然环境因素Ⅱ.多元回归分析与地带性研究[J].干旱区研究,2007,24(2):280-286.
[21]陈爱平,安和平.中国人口时间序列预测模型的探讨[J].人口与经济,2004,(6):63-67.
[22]薛臻.我国人口增长预测数学模型[J].河南科技学院学报(自然科学版),2008,36(1):123-127.
[23]周诗国.我国人口的灰色预测模型研究及其应用[J].数理医药学杂志,2005,18(4):307-309.
[24]蒿建华.灰色模型在人口预测中的应用[J].西安文理学院学报(社会科学版),2008,11(3):42-44.
[25]张静,王兴华.利用神经网络预测人口数量[J].襄樊学院学报,2001,22(5):73- 76.
[26]赵方,王晓雷,蔡森等.神经网络在人口自然率预测中的应用[J].中原工学院学报,2006,10,17(5):13-15.
[27]胡秋灵,姚文辉,李红霞.基于Box-Jenkins建模法的人口自然增长率预测模型[J].统计与决策,2007,(3):4-6.
[28]张静.基于Box-Jenkins建模法对中国人口增长率预测及结果分析[J].黑龙江科技信息,2009,(14):24-24.
[29]叶小青.人口问题的随机微分方程模型[J].统计与决策,2008,(6):161-162.
[30]李国成,吴涛,徐沈.灰色人工神经网络人口总量预测模型及应用[J].计算机工程与应用,2009,45(16):215-218.
[31]王丽敏,莫君慧.基于灰色BP神经网络的中国人口预测模型[J].新乡学院学报(自然科学版),2009,26(2):3-5.
[32]刘金月,许少华.基于自适应小波过程神经元网络的人口预测研究[J].长江大学学报(理工卷),2008,5(4):236-237,240.
[33]巩永丽,张德生,武新乾.人口增长率的非参数自回归预测模型[J].数理统计与管理,2007,26(5):759-764.
[34]姜爱平,张德生,武新乾等.预测我国人口总量的具有外生变量的半参数自回归模[J].河南科技大学学报(自然科学版),2007,28(1):97-100.
[35] Engk -lerF. RiceJ. Semiparametric estimates of the relation between weather and electricity sales [J]. Journal of the American Statistical Association ,1986,81:310-320.
[36] Paul,Speckman. Kemel smoothing in partial linear models[J]. Journal of the Royal Statistic Society:Series B, 1988,50:413-436.
[37] RiceJ. Convergence rates for partially splined models[J]. Statistics and Probability Letters,1986,4:203-208.
[38]王成勇.国内半参数回归模型研究进展[J].襄樊学院学报,2008,29(2):8-13.
[39]潘建敏.污染数据半参数回归模型的估计方法[J].工程数学学报,1997,14(3).
[40]薛留根.随机删失下半参数回归模型的估计理论[J].数学年刊(A辑),1999,20A(6):745-754.
[41]叶阿忠,吴相波,黄志刚.半参数计量经济联立模型的变窗宽估计理论[J].管理科学学报,2009,12(2):60-66.
[42]黄四民,梁华.用半参数部分线性模型分析居民消费结构[J].数量经济技术经济研究,1994,(10):33-38.
[43]王一兵.半参数回归模型在商品房价格指数中的应用研究[J].统计研究,2005,(4):25-29.
[44]冯春山,蒋馥,吴家春.应用半参数方法计算市场风险的受险价值[J].系统工程理论方法应用,2005,14(4):379-381.
[45]王学保,蔡果兰. Logistic模型的参数估计及人口预测[J].北京工商大学学报(自然科学版),2009,27 (6):75-78.
[46]彭志捌. AR(p)模型在中国总人口预测中的应用[J].河北工程大学学报(自然科学版), 2007, 24(4):109-112.
[47]叶阿忠.非参数计量经济学[M].南开大学出版社,2003.
[48]张慧芳,张德生,武新乾等.我国人口总量的非参数预测模型[J].延边大学学报(自然科学版),2007,33(2):90-93.
[49]武新乾,田铮,韩四儿.具有外生变量部分线性自回归模型的样条估计[J].数学年刊, 2007, 28A(3): 377-386.
[50]王振龙.时间序列分析[M].中国统计出版社,2000.
[51]李建民,王金营.中国生育率下降经济后果的计量分析[J].中国人口科学,2000,(1):8-16.
[52]王谦,郭震威.人口增长对经济增长的影响分析—与胡鞍钢博士商榷[J].人口研究, 2001, 25(1):20-23.
[53]冯利华.人口增长的综合预测分析[J].系统工程,2000,18(1):71-75.
[54]赵进文.中国人口总量与GDP总量关系模型的研究[J].中国人口科学,2003,(3):25-31.
[55]陈理洪.基于Copula函数的中国人口总量与GDP总量相关性研究[J].南阳师范学院学报,2008,7(9):27-28.
[56]姜爱平.我国人口时间序列的变系数预测模型[J].数理统计与管理, 2008, 27(5): 755-759.
[57] Efron,B. Bootstrap methods:Another look at the jackknife[J]. Annals of Statistics,1979, 7(1):1-26.
[58] Efron,B. An Introduction to the Bootstrap[M]. New York, Chapman and Hall, 1993.
[59] Yong P. Jackknife and bootstrap resampling methods in statistical analysis to correct for bias[J]. Statistical Science,1996,11:189-228.
[60] Bühlmann. P. Sieve bootstrap for time series[J]. Bernoulli 3,1997(1):123-148.
[61] Efron,B. The bootstrap and modern statistics[J]. Journal of the American Statistical Association, 2000,(1):1293-1296.
[62] Bühlmann. P. Bootstraps for time series[J]. Statistical Science,2002,17(1):52-72.
[63] Chang Y. J.Y.Park. A sieve bootstrap for the test of a unit root[J]. Journal of Time Series Analysis,2003,24(4):379-400.
[64] Politis,D.N. The impact of bootstrap methods on time series analysis[J]. Statistical Science,2003,18(2):219-230.
[65] James G. MacKinnon. Bootstrap Methods in Econometrics[J]. Queen’s Economics Department Working Paper No.1028,2006,(2):1-28.
[66] Jinhong You,Gemai Chen. Wild bootstrap estimation in partially linear models with beteroscedasticity[J]. Statistics & Probability Letters, 2006,76(4):340-348.
[67]龙志和,欧变玲. Bootstrap方法在经济计量领域的应用[J].工业技术经济,2008, 27(7):132-135.
[2]宋健,于景元.人口控制论[J].软科学研究,1989,(1):1-7.
[3]龚跃,党宏.人口预测的模型与方法[J].长春光学精密机械学院学报,1991,14(3):83-92.
[4]王伟华,宋宇婷,王福胜等.一类人口发展方程解的存在性和收敛性的研究[J].哈尔滨师范大学自然科学学报,2006,22(2):15-17.
[5]何朗,赵韫,管坤等.人口发展的参数预测模型[J].武汉理工大学学报(信息与管理工程版),2008,30(3):494-497.
[6]邹春松.“人口自然增长率”计算方法亟需改进[J].统计与决策,1991,(4):44-44.
[7]茆长宝,程琳.两种人口预测模型的精确度比较—以人口年龄移算法和灰色预测模型为例[J].南京人口管理干部学院学报,2009,(1):29-32.
[8]谢建文,张元标,王志伟等.基于宋健人口模型的老年化预测[J]. 2008,36(12):5227-5229.
[9]王勇. Logistic人口模型的求解问题[J].哈尔滨商业大学学报(自然科学版),2006,22(5):58-59.
[10]李百岁,同力嘎.内蒙古人口城市化Logistic模型及其应用[J].干旱区资源与环境,2007,21(2):32-36.
[11]冯守平.中国人口增长预测模型[J].安徽科技学院学报,2008,22(6):73-76.
[12]陈文权,赵兹,李得胜. Leslie修正模型在人口预测中的应用[J].世界科技研究与发展,2008,30(2):219-224.
[13] Lee R. D., Tuljapurkar, S. Stochastic Popultation Forecasts for the US Meetings of the Population[J]. Association of Amercia in Washington D.C., 1991.
[14] Lee. R.D. ,Carter L. Modeling and Forecasting US Moratlity[C]. Annual Meetings of the Population Association of America (Toronto),1990.
[15] Pollard.H.. Mathematical Models for the Grouth of Human Population[M].University Press, Cambridge,1975:112-134.
[16]李南,Tuljapurkar S.基于时间一区域序列的随机死亡率预测及对中国数据的应用[J].人口研究,1995,(4):58-63.
[17]李南,申卯兴.基于随机模型的中国生育率预测[J].预测,1996,15(6):33-36.
[18]李南,胡华清.基于随机方法的中国人口预测与规划[J].系统工程理论方法应用,1998,7(1):37-41.
[19]付莹.回归分析在人口预测中的应用[J].辽宁高职学报,2000,2(1):56-58.
[20]李旭东.贵州喀斯特高原人口分布的自然环境因素Ⅱ.多元回归分析与地带性研究[J].干旱区研究,2007,24(2):280-286.
[21]陈爱平,安和平.中国人口时间序列预测模型的探讨[J].人口与经济,2004,(6):63-67.
[22]薛臻.我国人口增长预测数学模型[J].河南科技学院学报(自然科学版),2008,36(1):123-127.
[23]周诗国.我国人口的灰色预测模型研究及其应用[J].数理医药学杂志,2005,18(4):307-309.
[24]蒿建华.灰色模型在人口预测中的应用[J].西安文理学院学报(社会科学版),2008,11(3):42-44.
[25]张静,王兴华.利用神经网络预测人口数量[J].襄樊学院学报,2001,22(5):73- 76.
[26]赵方,王晓雷,蔡森等.神经网络在人口自然率预测中的应用[J].中原工学院学报,2006,10,17(5):13-15.
[27]胡秋灵,姚文辉,李红霞.基于Box-Jenkins建模法的人口自然增长率预测模型[J].统计与决策,2007,(3):4-6.
[28]张静.基于Box-Jenkins建模法对中国人口增长率预测及结果分析[J].黑龙江科技信息,2009,(14):24-24.
[29]叶小青.人口问题的随机微分方程模型[J].统计与决策,2008,(6):161-162.
[30]李国成,吴涛,徐沈.灰色人工神经网络人口总量预测模型及应用[J].计算机工程与应用,2009,45(16):215-218.
[31]王丽敏,莫君慧.基于灰色BP神经网络的中国人口预测模型[J].新乡学院学报(自然科学版),2009,26(2):3-5.
[32]刘金月,许少华.基于自适应小波过程神经元网络的人口预测研究[J].长江大学学报(理工卷),2008,5(4):236-237,240.
[33]巩永丽,张德生,武新乾.人口增长率的非参数自回归预测模型[J].数理统计与管理,2007,26(5):759-764.
[34]姜爱平,张德生,武新乾等.预测我国人口总量的具有外生变量的半参数自回归模[J].河南科技大学学报(自然科学版),2007,28(1):97-100.
[35] Engk -lerF. RiceJ. Semiparametric estimates of the relation between weather and electricity sales [J]. Journal of the American Statistical Association ,1986,81:310-320.
[36] Paul,Speckman. Kemel smoothing in partial linear models[J]. Journal of the Royal Statistic Society:Series B, 1988,50:413-436.
[37] RiceJ. Convergence rates for partially splined models[J]. Statistics and Probability Letters,1986,4:203-208.
[38]王成勇.国内半参数回归模型研究进展[J].襄樊学院学报,2008,29(2):8-13.
[39]潘建敏.污染数据半参数回归模型的估计方法[J].工程数学学报,1997,14(3).
[40]薛留根.随机删失下半参数回归模型的估计理论[J].数学年刊(A辑),1999,20A(6):745-754.
[41]叶阿忠,吴相波,黄志刚.半参数计量经济联立模型的变窗宽估计理论[J].管理科学学报,2009,12(2):60-66.
[42]黄四民,梁华.用半参数部分线性模型分析居民消费结构[J].数量经济技术经济研究,1994,(10):33-38.
[43]王一兵.半参数回归模型在商品房价格指数中的应用研究[J].统计研究,2005,(4):25-29.
[44]冯春山,蒋馥,吴家春.应用半参数方法计算市场风险的受险价值[J].系统工程理论方法应用,2005,14(4):379-381.
[45]王学保,蔡果兰. Logistic模型的参数估计及人口预测[J].北京工商大学学报(自然科学版),2009,27 (6):75-78.
[46]彭志捌. AR(p)模型在中国总人口预测中的应用[J].河北工程大学学报(自然科学版), 2007, 24(4):109-112.
[47]叶阿忠.非参数计量经济学[M].南开大学出版社,2003.
[48]张慧芳,张德生,武新乾等.我国人口总量的非参数预测模型[J].延边大学学报(自然科学版),2007,33(2):90-93.
[49]武新乾,田铮,韩四儿.具有外生变量部分线性自回归模型的样条估计[J].数学年刊, 2007, 28A(3): 377-386.
[50]王振龙.时间序列分析[M].中国统计出版社,2000.
[51]李建民,王金营.中国生育率下降经济后果的计量分析[J].中国人口科学,2000,(1):8-16.
[52]王谦,郭震威.人口增长对经济增长的影响分析—与胡鞍钢博士商榷[J].人口研究, 2001, 25(1):20-23.
[53]冯利华.人口增长的综合预测分析[J].系统工程,2000,18(1):71-75.
[54]赵进文.中国人口总量与GDP总量关系模型的研究[J].中国人口科学,2003,(3):25-31.
[55]陈理洪.基于Copula函数的中国人口总量与GDP总量相关性研究[J].南阳师范学院学报,2008,7(9):27-28.
[56]姜爱平.我国人口时间序列的变系数预测模型[J].数理统计与管理, 2008, 27(5): 755-759.
[57] Efron,B. Bootstrap methods:Another look at the jackknife[J]. Annals of Statistics,1979, 7(1):1-26.
[58] Efron,B. An Introduction to the Bootstrap[M]. New York, Chapman and Hall, 1993.
[59] Yong P. Jackknife and bootstrap resampling methods in statistical analysis to correct for bias[J]. Statistical Science,1996,11:189-228.
[60] Bühlmann. P. Sieve bootstrap for time series[J]. Bernoulli 3,1997(1):123-148.
[61] Efron,B. The bootstrap and modern statistics[J]. Journal of the American Statistical Association, 2000,(1):1293-1296.
[62] Bühlmann. P. Bootstraps for time series[J]. Statistical Science,2002,17(1):52-72.
[63] Chang Y. J.Y.Park. A sieve bootstrap for the test of a unit root[J]. Journal of Time Series Analysis,2003,24(4):379-400.
[64] Politis,D.N. The impact of bootstrap methods on time series analysis[J]. Statistical Science,2003,18(2):219-230.
[65] James G. MacKinnon. Bootstrap Methods in Econometrics[J]. Queen’s Economics Department Working Paper No.1028,2006,(2):1-28.
[66] Jinhong You,Gemai Chen. Wild bootstrap estimation in partially linear models with beteroscedasticity[J]. Statistics & Probability Letters, 2006,76(4):340-348.
[67]龙志和,欧变玲. Bootstrap方法在经济计量领域的应用[J].工业技术经济,2008, 27(7):132-135.