Abstract: Attempt has been made in this research to apply generalized linear models in graduating China′s life table mortality rates.Using demographic data of deaths by age and gender from China Population Statistical Yearbooks 1995-2006 and Statistical Yearbooks of China′s Population and Employment 2007-2010,the relationships between mortality and age and between mortality and year are explored by fitting death rates at ages from 0 to 89 using Poisson regression and negative binomial regression.Upon comparison of the fitting effects of the two models,the paper proposes to use B-spline function to smooth the death rates.Implications of this study are discussed for constructing China′s empirical life tables,providing theoretical foundation and practical reference for mortality analysis by China Insurance Regulatory Commission,and achieving market-oriented rates of life insurance and scientific management of the life insurance industry in China.

Keywords: Mortality Rates, Generalized Linear Model, Negative Binomial Regression, Poisson Regression, B-spline Graduation

摘要： 基于GLM在我国国民生命表死亡率修匀中的应用,利用年鉴中全国分年龄、分性别死亡人口状况数据,将年龄和年份作为因子变量,研究死亡率与年龄和年份两因子之间的关系,采用GLM中的泊松回归模型、负二项回归模型对0～89岁的死亡率进行拟合,并对两种模型的拟合效果进行比较。实证分析结果表明,负二项回归模型的拟合效果优于泊松回归模型;进一步将年龄和年份两因子选为数值型变量,对数据进行光滑处理,在负二项回归模型下应用B-样条函数进行修匀。在我国人口死亡率修匀的应用研究中,基于GLM的动态死亡率修匀方法可发现近20年来我国分年龄、分性别死亡率变化规律,具有很强的适用性。由于可获得统计数据的局限性,无法对90岁及以上的死亡率进行修匀,随着人口数据的积累,未来将会在此方面有所改进。

关键词: 死亡率, 广义线性模型, 负二项回归, 泊松回归, B-样条修匀