In-sample forecasting with local linear survival densities

M. Hiabu, E. Mammen, M. D. Martìnez-Miranda and J. P. Nielsen

Biometrika, 2016, vol. 103, issue 4, 843-859

Abstract: In this paper, in-sample forecasting is defined as forecasting a structured density to sets where it is unobserved. The structured density consists of one-dimensional in-sample components that identify the density on such sets. We focus on the multiplicative density structure, which has recently been seen as the underlying structure of non-life insurance forecasts. In non-life insurance, the in-sample area is defined as one triangle and the forecasting area as the triangle which, added to the first triangle, completes a square. In recent approaches, two one-dimensional components are estimated by projecting an unstructured two-dimensional density estimator onto the space of multiplicatively separable functions. We show that time-reversal reduces the problem to two one-dimensional problems, where the one-dimensional data are left-truncated and a one-dimensional survival density estimator is needed. We then use the local linear density smoother with weighted crossvalidated and do-validated bandwidth selectors. Full asymptotic theory is provided, with and without time-reversal. Finite-sample studies and an application to non-life insurance are included.

Keywords: Aalen’s multiplicative model; Crossvalidation; Density estimation; Do-validation; Local linear kernel estimation; Survival data. (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (3)

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