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Generalised additive dependency inflated models including aggregated covariates

Lee, Y. K., Mammen, E., Nielsen, J. P. ORCID: 0000-0002-2798-0817 & Park, B. U. (2019). Generalised additive dependency inflated models including aggregated covariates. Electronic Journal of Statistics, 13(1), pp. 67-93. doi: 10.1214/18-ejs1515


Let us assume 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, λ(X)Y and X + Y for some unspecified function . 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 X, Y and the total waiting time X+Y . 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 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.

Publication Type: Article
Publisher Keywords: Structured nonparametric models, age-period-cohort model, identifiability, B-splines, UK mesothelioma mortality
Subjects: H Social Sciences > HA Statistics
H Social Sciences > HG Finance
Q Science > QA Mathematics
Departments: Bayes Business School > Actuarial Science & Insurance
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