论文标题
Lee-Carter家族的鲁棒参数估计：概率主成分方法
Robust Parameter Estimation for the Lee-Carter Family: A Probabilistic Principal Component Approach
论文作者
论文摘要
众所周知的Lee-Carter模型使用双线性形式$ \ log（m_ {x，t}）= a_x+b_xk_t $来表示对数死亡率，并在过去三十年中进行了广泛的研究和开发。但是，很少有人注意参数针对异常值的鲁棒性，尤其是在估计$ b_x $时。作为回应，我们为李 - 级式模型的广泛系列提出了一种强大的估计方法，将问题视为具有多元分布的概率主成分分析（PPCA）。还得出了有效的期望最大化（EM）算法以实现。 该方法的好处是三倍：1）它可以产生$ b_x $和$ k_t $，2）的更强大的估计值，它可以自然地扩展到李 - 卡特类型的大型型号，包括用于建模多个种群的模型，3）可以与其他现有的时间序列型$ k_t $集成。使用基于人类死亡率数据库的美国死亡率数据的数值研究，我们表明，在存在异常值的情况下，与常规方法相比，所提出的模型具有更强的功能。
The well-known Lee-Carter model uses a bilinear form $\log(m_{x,t})=a_x+b_xk_t$ to represent the log mortality rate and has been widely researched and developed over the past thirty years. However, there has been little attention being paid to the robustness of the parameters against outliers, especially when estimating $b_x$. In response, we propose a robust estimation method for a wide family of Lee-Carter-type models, treating the problem as a Probabilistic Principal Component Analysis (PPCA) with multivariate $t$-distributions. An efficient Expectation-Maximization (EM) algorithm is also derived for implementation. The benefits of the method are threefold: 1) it produces more robust estimates of both $b_x$ and $k_t$, 2) it can be naturally extended to a large family of Lee-Carter type models, including those for modelling multiple populations, and 3) it can be integrated with other existing time series models for $k_t$. Using numerical studies based on United States mortality data from the Human Mortality Database, we show the proposed model performs more robust compared to conventional methods in the presence of outliers.
