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Beyond Mean Modeling: Double GLMs and GAMs for Location, Scale and Shape (GAMLSS)

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Effective Statistical Learning Methods for Actuaries I

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Abstract

In this chapter, the modeling of the mean response is supplemented with additional scores linked to other parameters of the distribution, like dispersion, scale, shape or probability mass at the origin, for instance. This allows the actuary to let the available information enter other dimensions of the response, such as volatility or no-claim probability. The double GLM setting supplements GLMs with dispersion modeling, letting the dispersion parameter depend on the available features through a second, linear score. GAMs for location, scale and shape (GAMLSS) extend this construction to very general models, beyond mean and dispersion modeling, with additive scores including nonlinear effects of some features.

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Notes

  1. 1.

    Loess stands for Locally Weighted Scatterplot Smoother.

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Correspondence to Michel Denuit .

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Denuit, M., Hainaut, D., Trufin, J. (2019). Beyond Mean Modeling: Double GLMs and GAMs for Location, Scale and Shape (GAMLSS). In: Effective Statistical Learning Methods for Actuaries I. Springer Actuarial(). Springer, Cham. https://doi.org/10.1007/978-3-030-25820-7_7

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