Local linear density estimation for filtered survival data, with bias correction
| Autor: | Carsten Tanggaard, Jens Perch Nielsen, M. C. Jones |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2009 |
| Předmět: |
Statistics and Probability
Pointwise old age mortality exposure robustness Multiplicative function Kernel density estimation Estimator Density estimation Censoring (statistics) Weighting Aalen's multiplicative model Additive bias correction Censoring Counting processes Exposure robustness Multiplicative bias correction censoring Survival function additive bias correction Statistics Applied mathematics multiplicative bias correction Truncation (statistics) counting processes kernel density estimation Statistics Probability and Uncertainty Mathematics |
| Zdroj: | Nielsen, J P, Tanggaard, C & Jones, M C 2009, ' Local linear density estimation for filtered survival data, with bias correction ', Statistics, vol. 43, no. 2, pp. 167-186 . https://doi.org/10.1080/02331880701736648 |
| ISSN: | 0233-1888 |
| DOI: | 10.1080/02331880701736648 |
| Popis: | 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 the 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. 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 the 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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