Local Linear Density Estimation for Filtered Survival Data, with Bias Correction

Jens Perch Nielsen (), Carsten Tanggaard () and M. C. Jones
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Jens Perch Nielsen: Royal & SunAlliance, Codan, Postal: Gammel Kongevej 60,, 1790 København V,, Denmark
Carsten Tanggaard: Department of Finance, Aarhus School of Business, Postal: The Aarhus School of Business, Fuglesangs Allé 4, 8210 Aarhus V, Denmark, http://www.asb.dk/departments/fin/staff/academic/cat.htm
M. C. Jones: Department of Statistics, Open University, Postal: Milton Keynes MK7 6AA,, United Kingdom

No 03-9, Finance Working Papers from University of Aarhus, Aarhus School of Business, Department of Business Studies

Abstract: A class of local linear kernel density estimators based on weighted least squares kernel estimation is considered within the framework of Aalen's multiplicative intensity model. This model includes the filtered data model that, in turn, allows for truncation and/or censoring in addition to accomodating unusual patterns of exposure as well as occurrence. It is shown that the local linear estimators corresponding to all different weightings have the same pointwise asymptotic properties. However, the weighting previously used in the literature in the i.i.d. case is seen to be far from optimal when it comes to exposure robustness, and a simple alternative weighting is to be preferred. Indeed, this weighting has, effectively, to be well chosen in a 'pilot' estimator of the survival funcition as well as in the main estimator itself. We also investigate multiplicative and additive bias correction methods within our framework. The multiplicative bias correction method proves to be best in a simulation study comparing the performance of the considered estimators.

Keywords: Aalen's multiplicative model; Additive bias correction; Censoring; Counting processes; Exposure robustness; Kernel density estimation; Multiplicative bias correction (search for similar items in EconPapers)
Pages: 30 pages
Date: 2003-12-01
New Economics Papers: this item is included in nep-ecm and nep-hea
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