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

Author

Listed:
  • Nielsen, Jens Perch

    (Royal & SunAlliance, Codan)

  • Tanggaard, Carsten

    (Department of Finance, Aarhus School of Business)

  • Jones, M. C.

    (Department of Statistics, Open University)

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.

Suggested Citation

  • Nielsen, Jens Perch & Tanggaard, Carsten & Jones, M. C., 2003. "Local Linear Density Estimation for Filtered Survival Data, with Bias Correction," Finance Working Papers 03-9, University of Aarhus, Aarhus School of Business, Department of Business Studies.
    • Handle: RePEc:hhb:aarfin:2003_009
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    File URL: http://www.hha.dk/fin/cms/wp/D03_9.pdf
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    References listed on IDEAS

    as
    1. Lejeune, Michel & Sarda, Pascal, 1992. "Smooth estimators of distribution and density functions," Computational Statistics & Data Analysis, Elsevier, vol. 14(4), pages 457-471, November.
    2. Jens Perch Nielsen & Carsten Tanggaard, 2001. "Boundary and Bias Correction in Kernel Hazard Estimation," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 28(4), pages 675-698, December.
    3. Perch Nielsen, Jens & Tanggaard, Carsten, 2000. "Boundary and Bias Correction in Kernel Hazard Estimation," Finance Working Papers 00-7, University of Aarhus, Aarhus School of Business, Department of Business Studies.
    4. Linton, Oliver & Nielsen, Jens Perch, 1994. "A multiplicative bias reduction method for nonparametric regression," Statistics & Probability Letters, Elsevier, vol. 19(3), pages 181-187, February.
    Full references (including those not matched with items on IDEAS)

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