SEMIPARAMETRIC CONTINUOUS MORTALITY MODELING VIA GAUSSIAN PROCESS RESIDUAL CORRECTION ON TMPI 2023

Abstract

The Indonesian Population Mortality Table 2023 (TMPI 2023) provides graduated annual death probabilities at integer ages. This study proposes a semiparametric framework that combines a parametric backbone with a Gaussian Process (GP) correction of log-space residuals to construct continuous mortality functions for male and female populations. Two backbone families are considered: Gompertz and Heligman–Pollard, with fixed eight- and five-parameter variants of the latter. A Matérn $\nu = 5/2$ GP is fitted to residuals of annual cumulative hazards using an interval approximation. Annual death probabilities and survival are derived from a common integrated force, and curtate expectancy is distinguished from complete expectancy restricted to age 111. Evaluation uses 111 annual probabilities per sex and leave-one-age-out cross-validation that refits both the backbone and GP on each training set. Gompertz+GP achieves the lowest LOO RMSE among the evaluated candidates: $3.58881 \times 10^{-5}$ for males and $3.24246 \times 10^{-5}$ for females, compared with $0.00648539$ and $0.00590577$ for Gompertz alone. The absolute birth curtate-expectancy errors are below $0.16\%$ for the three GP-corrected specifications. These results support reconstruction of missing ages within the published table. Conditional pointwise latent-force intervals are provided, while source-estimation uncertainty, active parameter constraints, and within-year approximation limit the interpretation.