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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 one-dimensional 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.
|Additional Information:||This is a pre-copyedited, author-produced PDF of an article accepted for publication in Biometrika, following peer review. The version of record Munir, H., Mammen, E., Martinez-Miranda, M. D. & Nielsen, J. P. (2016). In-Sample Forecasting with Local Linear Survival Densities. Biometrika, will be available online at: http://biomet.oxfordjournals.org/|
|Uncontrolled Keywords:||Aalen’s multiplicative model; Cross-validation; Do-validation; Density estimation; Local linear kernel estimation; Survival data|
|Subjects:||H Social Sciences > HA Statistics|
|Divisions:||Cass Business School > Faculty of Actuarial Science & Insurance|
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