In mortality modelling, cohort effects are often taken into consideration as they add insights about variations in mortality across different generations. Statistically speaking, models such as the Renshaw-Haberman model may provide a better fit to historical data compared to their counterparts that incorporate no cohort effects. However, when such models are estimated using an iterative maximum likelihood method in which parameters are updated one at a time, convergence is typically slow and may not even be reached within a reasonably established maximum number of iterations. Among others, the slow convergence problem hinders the study of parameter uncertainty through bootstrapping methods. In this paper, we propose an intuitive estimation method that minimizes the sum of squared errors between actual and fitted log central death rates. The complications arising from the incorporation of cohort effects are overcome by formulating part of the optimization as a principal component analysis with missing values. We also show how the proposed method can be generalized to variants of the Renshaw-Haberman model with further computational improvement, either with a simplified model structure or an additional constraint. Using mortality data from the Human Mortality Database (HMD), we demonstrate that our proposed method produces satisfactory estimation results and is significantly more efficient compared to the traditional likelihood-based approach.

翻译：在死亡率建模中，队列效应常被纳入考量，因其可揭示不同世代间死亡率变化的深层规律。从统计学角度看，与未包含队列效应的模型相比，Renshaw-Haberman等模型能更优地拟合历史数据。然而，当采用逐一更新参数的迭代最大似然法进行估计时，此类模型的收敛速度通常较慢，甚至在预设的最大迭代次数内无法收敛。其中，收敛缓慢的问题尤其阻碍了通过自助法研究参数不确定性。本文提出一种直觉性估计方法，通过最小化实际与拟合对数中心死亡率之间的平方误差总和。我们将部分优化问题转化为含缺失值的主成分分析，从而克服了引入队列效应带来的复杂性。进一步地，我们展示了如何将该方法推广至Renshaw-Haberman模型的各类变体——通过简化模型结构或附加约束条件，实现计算效率的进一步提升。基于人类死亡率数据库（HMD）的实证分析表明：本方法既能获得满意的估计结果，其计算效率也显著优于传统的似然函数方法。