In-sample forecasting with local linear survival densities
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 bee...
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| Main Authors: | , , , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
08 December 2016
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| In: |
Biometrika
Year: 2016, Volume: 103, Issue: 4, Pages: 843-859 |
| ISSN: | 1464-3510 |
| DOI: | 10.1093/biomet/asw038 |
| Online Access: | Verlag, Volltext: http://dx.doi.org/10.1093/biomet/asw038 Verlag, Volltext: https://academic.oup.com/biomet/article/103/4/843/2659029 
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| Author Notes: | M. Hiabu, E. Mammen, M.D. Martìnez-Miranda, J.P. Nielsen |
| Summary: | 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. |
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| Item Description: | Gesehen am 15.01.2018 |
| Physical Description: | Online Resource |
| ISSN: | 1464-3510 |
| DOI: | 10.1093/biomet/asw038 |