Multidimensional smoothing by adaptive local kernel-weighted log-likelihood with application to long-term care insurance

The present article illustrates how adaptive local likelihood methods can be applied to ultidimensional smoothing. We are interested in the variation of mortality of individuals subscribing long-term care insurance. We analyze the incidence of mortality as a function of both the age of occurrence of the pathology and the duration of the care. Individuals under long-term care insurance are marked by a relatively strong mortality pattern. Hence rather than restricting the smoothing parameters to a fixed value and over-smoothing the mortality surface, a more flexible approach is to allow the constellation of smoothing parameters to vary across the age of occurrence and the duration of the care. We distinguish the intersection of confidence intervals rule and local bandwidth correction factors. We vary the amount of smoothing in a location dependent manner and allow adjustments based on the reliability of the data. Tests, and single indices summarizing the life time probability distribution are used to compare the graduated series obtained by adaptive local kernel-weighted log-likelihoods to P-splines and local likelihood models.