This is the accepted version of the paper.This version of the publication may differ from the final published version. 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 that 20 added to the first triangle produces a square. Recent approaches estimate two one-dimensional components 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 onedimensional problems, where the one-dimensional data are left-truncated and a one-dimensional survival density estimator is needed. This paper then uses the local linear density smoother with 25 weighted cross-validated 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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This is the accepted version of the paper.This version of the publication may differ from the final published version.
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AbstractIn this paper we propose a method close to Double Chain Ladder (DCL) introduced in Martínez-Miranda, Nielsen and Verrall (2012). The proposed method is motivated by the potential lack of stability of Double Chain Ladder (and of the classical Chain ladder method itself). We consider the implicit estimation of the underwriting year inflation in the classical Chain Ladder (CLM) method and the explicit estimation of it in DCL. This may represent a weak point for DCL and CLM because the underwriting year inflation might be estimated with significant uncertainty. A key feature of the new method is that the underwriting year inflation can be estimated from the less volatile incurred data and then transferred into the DCL model. We include an empirical illustration which illustrates the differences between the estimates of the IBNR and RBNS cash flows from DCL and the new method. We also apply bootstrap estimation to approximate the predictive distributions.
Citation: Martinez-Miranda, M. D., Nielsen, B. & Nielsen, J. P. (2016). A simple benchmark for mesothelioma projection for Great Britain. Occupational and Environmental Medicine, 73, pp. 561-563. doi: 10.1136/oemed-2015-103303 This is the accepted version of the paper.This version of the publication may differ from the final published version. The response-only model has 5% higher peak mortality than the dose-response model. The former performs slightly better in out-of-sample comparison.
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Modelling the first-order intensity function is one of the main aims in point process theory, and it has been approached so far from different perspectives. One appealing model describes the intensity as a function of a spatial covariate. In the recent literature, estimation theory and several applications have been developed assuming this model, but without formally checking this assumption. In this paper we address this problem for a non-homogeneous Poisson point process, by proposing a new test based on an L 2 -distance. We also prove the asymptotic normality of the statistic and we suggest a bootstrap procedure to accomplish the calibration. Two applications with real data are presented and a simulation study to better understand the performance of our proposals is accomplished. Finally some possible extensions of the present work to non-Poisson processes and to a multi-dimensional covariate context are detailed. arXiv:1709.07716v2 [stat.ME]
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