Generalised additive dependency inflated models including aggregated covariates - Lee, Young K.; Mammen, Enno; Nielsen, Jens P.; Park, Byeong U. (Electronic journal of statistics, 2019)
Let us assume that XXX, YYY and UUU are observed and that the conditional mean of UUU given XXX and YYY can be expressed via an additive dependency of XXX, λ(X)Yλ(X)Yλ(X)Y and X+YX+YX+Y for some unspecified function λλλ. This structured regression model can be transferred to a hazard model or a density model when applied on some appropriate grid, and has important forecasting applications via structured marker dependent hazards models or structured density models including age-period-cohort relationships. The structured regression model is also important when the severity of the dependent variable has a complicated dependency on waiting times XXX, YYY and the total waiting time X+YX+YX+Y. In case the conditional mean of UUU approximates a density, the regression model can be used to analyse the age-period-cohort model, also when exposure data are not available. In case the conditional mean of UUU approximates a marker dependent hazard, the regression model introduces new relevant age-period-cohort time scale interdependencies in understanding longevity. A direct use of the regression relationship introduced in this paper is the estimation of the severity of outstanding liabilities in non-life insurance companies. The technical approach taken is to use B-splines to capture the underlying one-dimensional unspecified functions. It is shown via finite sample simulation studies and an application for forecasting future asbestos related deaths in the UK that the B-spline approach works well in practice. Special consideration has been given to ensure identifiability of all models considered.