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Fly-By-Night Life Insurance and the NPMLE for Weibull Frailty Models

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Fly-By-Night Life Insurance and the NPMLE for Weibull Frailty Models
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13
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CC Attribution - NonCommercial - NoDerivatives 4.0 International:
You are free to use, copy, distribute and transmit the work or content in unchanged form for any legal and non-commercial purpose as long as the work is attributed to the author in the manner specified by the author or licensor.
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Unobserved heterogeneity is an common feature of statistical survival analysis where it is usually referred to as frailty. Parametric mixture models are frequently used to capture these effects, but it is desirable to consider nonparametric mixture models as well. We illustrate the latter approach with a reanalysis of a large scale mortality study of Mediterranean fruit flies employing the Kiefer-Wolfowitz nonparametric maximum likelihood estimator of the mixing distribution for a nonparametric Weibull frailty model. Empirical Bayes methods are employed to design actuarially fair life insurance contracts to contrast the approach with parametric methods. Some associated problems of profile likelihood will also be addressed.