本文结合Bootstrap方法与Lee-Carter模型对我国人口死亡率进行拟合与预测，较好地解决了传统模型的不足.首先利用最小二乘法、加权最小二乘法和极大似然法三种参数估计方法对Lee-Carter模型的参数进行估计.然后通过对残差的分布性质进行分析发现加权最小二乘法有较好的拟合效果.再考虑到传统的Lee-Carter模型在预测未来死亡率区间时仅考虑了时间参数的变动区间，因此利用残差Bootstrap方法估计了所有参数的置信区间，并对模型参数的稳健性进行检验.最后在充分考虑所有参数变动性的基础上，给出了死亡率预测均值及死亡率预测值的置信区间，结果表明，所计算的死亡率预测值的置信区间具有更好的预测效果.
Abstract
In this paper, we apply the Bootstrap method combined with Lee-Carter model, which fits and forecasts the population mortality in our country, and better solves the deficiency of the traditional model. At first, the least squares, weighted least squares and maximum likelihood parameter estimation method are used to estimate the parameters of the model. By the analysis of the distribution of the model residual, we can know that the weighted least squares method has a better fitting effect. Secondly, in the prediction of confidence interval, traditional Lee-Carter model only takes the variability of the time parameter into consideration. Instead, we use the residual Bootstrap method to estimate the confidence interval of all parameters, and test the robustness of model parameters. Finally, by fully considering all parameters variability, the confidence interval of predicted mortality and predicted mean mortality are given, and the results show that the confidence interval has better fitness of prediction.
关键词
死亡率预测 /
Lee-Carter模型 /
Bootstrap方法 /
置信区间
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Key words
prediction of mortality /
Lee-Carter model /
Bootstrap method /
confidence interval
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中图分类号：
O213
F840
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参考文献
[1] Lee R D, Carter L R. Modeling and forecasting US mortality[J]. Journal of the American Statistical Association, 1992, 87(419):659-671.
[2] Wilmoth J R. Computational methods for fitting and extrapolating the Lee-Carter model of mortality change[R]. Technical Report. Berkeley:University of California, 1993.
[3] Wilmoth J R. Mortality projections for Japan:A comparison of four methods[M]. New York:Oxford University Press, 1996.
[4] Brouhns N, Denuit M, Vermunt J. A Poisson log-linear regression approach to the construction of projected life tables[J]. Insurance:Mathematics and Economics, 2002, 31:373-393.
[5] Tuljapurkar S, Nan L, Boe C. A universal pattern of mortality decline in the G7 countries[J]. Nature, 2002, 405:789-792.
[6] Renshaw A E, Haberman S. A cohort-based extension to the Lee-Carter model for mortality reduction factors[J]. Insurance:Mathematics and Economics, 2006, 38:556-570.
[7] 王晓军,蔡正高. 死亡率预测模型的新进展[J]. 统计研究, 2008, 25:80-83. Wang X J, Cai Z G. New developments on mortality projection model[J]. Statistical Research, 2008, 25:80-83.
[8] 卢仿先, 尹莎. Lee-Carter方法在预测中国人口死亡率中的应用[J]. 保险职业学院学报, 2005, 6:9-11.
[9] 祝伟, 陈秉正. 中国城市人口死亡率的预测[J]. 数理统计与管理, 2009, 28:736-744. Zhu W, Chen B Z. Mortality projection of Chinese urban population[J]. Application of Statistics and Management, 2009, 28:736-744.
[10] 田梦, 邓颖璐. 我国随机死亡率的长寿风险建模和衍生品定价[J]. 保险研究, 2013, 1:14-26. Tian M, Deng Y L. Longevity risk modeling and derivatives pricing based on China mortality rate[J]. Insurance Studies, 2013, 1:14-26.
[11] 李志生, 刘恒甲. Lee-Carter死亡模型的估计与应用——基于中国人口数据的分析[J]. 中国人口科学, 2010, 3:46-56. Li Z S, Liu H J. Estimation and application of the Lee-Carter model:Based on demographic data of China[J]. Chinese Journal of Population Science, 2010, 3:46-56.
[12] 王晓军, 任文东. 有限数据下Lee-Carter模型在人口死亡率预测中的应用[J]. 统计研究, 2012, 29:87-94. Wang X J, Ren W D. Application of Lee-Carter method in forecasting the mortality of Chinese population with limited data[J]. Statistical Research, 2012, 29:87-94.
[13] 孙佳美, 段白鸽. Bootstrap方法在死亡模型中的应用[J]. 统计研究, 2010, 27:101-105. Sun J M, Duan B G. The application of bootstrap method in mortality model[J]. Statistical Research, 2010, 27:101-105.
[14] Goodman L A. Simple models for the analysis of association in cross-classifications having ordered categories[J]. Journal of the American Statistical Association, 1979, 74:537-552.
[15] Renshaw A E, Haberman S. On the forecasting of mortality reduction factors[J]. Insurance:Mathematics and Economics, 2003, 32:379-401.
[16] Olkin I. Contributions to probability and statistics:Essays in honor of Harold Hoteling[M]. California:Stanford University Press, 1960:278-292.
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脚注
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基金
国家自然科学基金（71571195）；教育部人文社会科学研究青年基金（12YJCZH267）；霍英东教育基金会高等院校青年教师基金（151081）；广东省自然科学杰出青年基金（2015A030306040）
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