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Identification and forecasting in mortality models. (English) Zbl 1328.62575

Summary: Mortality models often have inbuilt identification issues challenging the statistician. The statistician can choose to work with well-defined freely varying parameters, derived as maximal invariants in this paper, or with ad hoc identified parameters which at first glance seem more intuitive, but which can introduce a number of unnecessary challenges. In this paper, we describe the methodological advantages from using the maximal invariant parameterisation and we go through the extra methodological challenges a statistician has to deal with when insisting on working with ad hoc identifications. These challenges are broadly similar in frequentist and in Bayesian setups. We also go through a number of examples from the literature where ad hoc identifications have been preferred in the statistical analyses.

MSC:

62P05 Applications of statistics to actuarial sciences and financial mathematics
91B30 Risk theory, insurance (MSC2010)

Software:

R
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