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Title: Generalised additive dependency inflated models including aggregated covariate Authors:  Young Kyung Lee - Kangwon National University (Korea, South) [presenting]
Enno Mammen - University of Heidelberg (Germany)
Jens Perch Nielsen - Cass Business School (United Kingdom)
Byeong Park - Seoul National University (Korea, South)
Abstract: Suppose that $X$, $Y$ and $U$ are observed and that the conditional mean of $U$ given $X$ and $Y$ can be expressed via an additive dependency of $X$, $\lambda(X)Y$ and $X+Y$ for some unspecified function $\lambda$. 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 density models including age-period-cohort relationships. In case the conditional mean of $U$ 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 $U$ 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 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 1-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.