## Electronic Journal of Statistics

### Generalised additive dependency inflated models including aggregated covariates

#### 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.

#### Article information

Source
Electron. J. Statist., Volume 13, Number 1 (2019), 67-93.

Dates
First available in Project Euclid: 4 January 2019

https://projecteuclid.org/euclid.ejs/1546570942

Digital Object Identifier
doi:10.1214/18-EJS1515

Mathematical Reviews number (MathSciNet)
MR3896146

Zentralblatt MATH identifier
07003258

Subjects
Primary: 62G08: Nonparametric regression
Secondary: 62G20: Asymptotic properties

#### Citation

Lee, Young K.; Mammen, Enno; Nielsen, Jens P.; Park, Byeong U. Generalised additive dependency inflated models including aggregated covariates. Electron. J. Statist. 13 (2019), no. 1, 67--93. doi:10.1214/18-EJS1515. https://projecteuclid.org/euclid.ejs/1546570942

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