随机死亡率模型的改进与预测  

Improving the Stochastic Mortality Model and Its Forecasing:A Change-point Detection of Principal Component Scores

作　　者：张志强[1] 杨帆[2] 

机构地区：[1]厦门大学经济学院统计系 [2]厦门大学经济学院

出　　处：《中国人口科学》2017年第2期47-59,共13页Chinese Journal of Population Science

基　　金：国家社会科学基金重大项目"大数据与统计学理论的发展研究"(编号:13&ZD148)的阶段性成果

摘　　要：文章将多变点检测方法应用于人口死亡率预测,并对年龄别死亡率的偏差进行主成分提取,利用变点检测法分别估计了主要主成分得分随时间变化的最优变点个数及位置,据此对主成分得分进行分段线性回归拟合,从最后一段回归模型外推主成分得分的预测值,得到死亡率预测值;同时利用发达国家1951~2010年连续60年死亡率数据,对改进的PC模型与经典Lee-Carter进行比较研究,结果表明,改进的PC模型在死亡率预测的精度和稳定性方面均优于经典Lee-Carter模型,多变点检测方法提高了死亡率模型的预测精度。研究结果显示,基于奇异值分解的经典Lee-Carter模型中的时间因子和基于特征值分解的经典PC模型中的第一主成分得分反映出了几乎一致的死亡率变化趋势;经典PC模型中的第二主成分主要综合了队列效应对死亡率的影响。The paper uses the multiple change-point detection method to forecast population mortality. The principal component extraction is performed on the deviation of age mortality, and change-point detection method is used to estimate the number of the optimal change points and the location of the change points of the main principal component scores with time. Then the principal component scores are fitted by piecewise linear regression, and predicted values of the principal component scores are extrapolated according to the last regression model, which can be taken into the classical PC model to obtain the predicted mortality. Using 1951-2010 mortality data for 60 consecutive years in developed countries to compare the improved PC model with the classic Lee-Carter model, the results show that the improved PC model is superior to the classical Lee-Carter model in accuracy and stability of mortality prediction, and the multiple change-point detection method improves the prediction accuracy of the mortality model. The time factor of the classical Lee-Carter model based on singular value decomposition and the first principal component of the classical PC model based on eigenvalue decomposition reflect the almost uniform trend of mortality change. The second principal component of the classical PC model synthesizes the influence of cohort effect on mortality.

关 键 词：随机死亡率 主成分分析 变点检测 队列效应 分段线性回归 

分 类 号：C921[社会学—人口学]