In-sample forecasting with local linear survival densities

• 成果类型: Article
• 署名作者: Hiabu, M.; Mammen, E.; Martinez-Miranda, M. D.; Nielsen, J. P.
• 署名单位: City St Georges, University of London; Ruprecht Karls University Heidelberg
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asw038
• 发表日期: 2016
• 页码: 843859
• 关键词: cross-validation; chain-ladder; prediction; MODEL

摘要

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.