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Kernel density estimation of actuarial loss functions. (English) Zbl 1024.62041

Summary: We estimate actuarial loss functions based on a symmetrized version of the semiparametric transformation approach to kernel smoothing. We apply this method to an actuarial study of automobile claims. The method gives a good overall impression while estimating actuarial loss functions, since it is capable of estimating both the initial mode and the heavy tail that is so typical for actuarial and other economic loss distributions.
We study the properties of the transformation kernel density estimation and show the differences with the multiplicative bias corrected estimator. We add insight into the kernel smoothing transformation method through an extensive simulation study with a particular view to the performance of the estimation at the tail.

MSC:

62P05 Applications of statistics to actuarial sciences and financial mathematics
62G07 Density estimation

Software:

KernSmooth
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References:

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