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A new inference strategy for general population mortality tables. (English) Zbl 1444.91190

Summary: We propose a new inference strategy for general population mortality tables based on annual population and death estimates, completed by monthly birth counts. We rely on a deterministic population dynamics model and establish formulas that link the death rates to be estimated with the observables at hand. The inference algorithm takes the form of a recursive and implicit scheme for computing death rate estimates. This paper demonstrates both theoretically and numerically the efficiency of using additional monthly birth counts for appropriately computing annual mortality tables. As a main result, the improved mortality estimators show better features, including the fact that previous anomalies in the form of isolated cohort effects disappear, which confirms from a mathematical perspective the previous contributions by S. J. Richards [“Detecting year-of-birth mortality patterns with limited data”, J. R. Stat. Soc. Ser. A 171, No. 1, 279–298 (2007; doi:10.1111/j.1467-985x.2007.00501.x)], A. J. G. Cairns et al. [“Phantoms never die: living with unreliable population data”, J. R. Stat. Soc. Ser. A 179, No. 4, 975–1005 (2016; doi:10.1111/rssa.12159)], and A. Boumezoued [“Improving HMD mortality estimates with HFD fertility data”, N. Am. Actuar. J. (to appear) (doi:10.1080/10920277.2019.1672567)].

MSC:

91G05 Actuarial mathematics
91D20 Mathematical geography and demography
62P05 Applications of statistics to actuarial sciences and financial mathematics
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