  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.

Methodology;Applications