Estimation of a semiparametric multiplicative density model

This paper discusses the estimation of a semiparametric structured density model that is very useful in forecasting the density on a region where the data are not observed. The model has many applications in actuarial science and mortality forecasting. It has a multiplicative structure with both parametric and nonparametric components that can be estimated based on the data at hand. The problem of estimating the parametric component is nonstandard since the information about the parametric component can be gathered through the derivative of the nonparametric components that are hard to estimate. We propose a simple procedure of estimating the parametric component, which may be used to construct estimators of the nonparametric components. We show that our estimator is consistent with a certain rate and also that it works quite well for finite sample sizes.