Local Linear Density Estimation for Filtered Survival Data, with Bias Correction
Centre for Analytical Finance Working Paper No. 185
38 Pages Posted: 11 Dec 2004
Date Written: September 2004
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 accommodating 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 function 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. An example concerning old age mortality demonstrates the importance of the improvements provided.
Keywords: Aalen's multiplicative model, additive bias correction, censoring, counting processes, exposure robustness, kernel density estimation, multiplicative bias correction, old age mortality
JEL Classification: C13, C14
Suggested Citation: Suggested Citation