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2019 Generalised additive dependency inflated models including aggregated covariates
Young K. Lee, Enno Mammen, Jens P. Nielsen, Byeong U. Park
Electron. J. Statist. 13(1): 67-93 (2019). DOI: 10.1214/18-EJS1515

Abstract

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 $X$, $\lambda(X)Y$ 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 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.

Citation

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Young K. Lee. Enno Mammen. Jens P. Nielsen. Byeong U. Park. "Generalised additive dependency inflated models including aggregated covariates." Electron. J. Statist. 13 (1) 67 - 93, 2019. https://doi.org/10.1214/18-EJS1515

Information

Received: 1 December 2017; Published: 2019
First available in Project Euclid: 4 January 2019

zbMATH: 07003258
MathSciNet: MR3896146
Digital Object Identifier: 10.1214/18-EJS1515

Subjects:
Primary: 62G08
Secondary: 62G20

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Vol.13 • No. 1 • 2019
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