In-sample forecasting with local linear survival densities

• Verfasst von: Hiabu, Munir [VerfasserIn]
• Verfasst von: Mammen, Enno [VerfasserIn]
• Verfasst von: Martinez Miranda, Maria Dolores [VerfasserIn]
• Verfasst von: Nielsen, Jens Perch [VerfasserIn]
• Titel: In-sample forecasting with local linear survival densities
• Verf.angabe: M. Hiabu, E. Mammen, M.D. Martìnez-Miranda, J.P. Nielsen
• Umfang: 17 S.
• Fussnoten: Gesehen am 15.01.2018
• Titel Quelle: Enthalten in: Biometrika
• Jahr Quelle: 2016
• Band/Heft Quelle: 103(2016), 4, S. 843-859
• ISSN Quelle: 1464-3510
• DOI: doi:10.1093/biomet/asw038
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 1567168116

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.