Robust Parameter Estimation for the Lee-Carter Family: A Probabilistic Principal Component Approach

2022/02/10 by Yiping Guo, Guo, Yiping, Johnny Siu‐Hang Li +1
Social Sciences · Decision Sciences · Mathematics · #Insurance, Mortality, Demography, Risk Management #Forecasting Techniques and Applications #Statistical Methods and Bayesian Inference

paper · pdf · doi:10.48550/arxiv.2202.05349

Abstract

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.

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