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

See all articles by Jens Perch Nielsen

Jens Perch Nielsen

City University London - Cass Business School

Carsten Tanggaard

affiliation not provided to SSRN

M. C. Jones

The Open University

Date Written: September 2004

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 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

Nielsen, Jens Perch and Tanggaard, Carsten and Jones, M. C., Local Linear Density Estimation for Filtered Survival Data, with Bias Correction (September 2004). Centre for Analytical Finance Working Paper No. 185. Available at SSRN: https://ssrn.com/abstract=630003 or http://dx.doi.org/10.2139/ssrn.630003

Jens Perch Nielsen (Contact Author)

City University London - Cass Business School ( email )

106 Bunhill Row
London, EC1Y 8TZ
United Kingdom

Carsten Tanggaard

affiliation not provided to SSRN

M. C. Jones

The Open University ( email )

Walton Hall
Milton Keynes, MK6 7AA
United Kingdom

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