Robust parameter estimation for the Lee-Carter family: A probabilistic principal component approach
提出一种基于概率主成分分析和多元t分布的稳健估计方法，用于Lee-Carter模型及其多人口扩展，能有效抵抗异常值对年龄特定参数估计的干扰，并保持模型的双线性项作为第一主成分的解释力。
Although the impact of outliers on stochastic mortality modelling has been examined, previous studies on this topic focus on how outliers in the estimated time-varying indexes may be detected and/or modelled, with little attention being paid to the adverse effects of outliers on estimation robustness, particularly that pertaining to age-specific parameters. In this paper, we propose a robust estimation method for the Lee-Carter model, through a reformulation of the model into a probabilistic principal component analysis with multivariate t -distributions and an efficient expectation-maximization algorithm for implementation. The proposed method yields significantly more robust parameter estimates, while preserving the fundamental interpretation for the bilinear term in the model as the first principal component and the flexibility of pairing the estimated time-varying parameters with any appropriate time-series process. We also extend the proposed method for use with multi-population generalizations of the Lee-Carter model, allowing for a wider range of applications such as quantification of population basis risk in index-based longevity hedges. Using a combination of real and pseudo datasets, we demonstrate the superiority of the proposed method relative to conventional estimation approaches such as singular value decomposition and maximum likelihood.