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Smoothing survival densities in practice

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  • Gámiz Pérez, M. Luz
  • Martínez Miranda, María Dolores
  • Nielsen, Jens Perch

Abstract

Many nonparametric smoothing procedures consider independent identically distributed stochastic variables. There are also many important nonparametric smoothing applications where the data is more complicated. Survival data or filtered data, defined as following Aalen’s multiplicative hazard model and aggregated versions of this model, are considered. Aalen’s model based on counting process theory allows multiple left truncations and multiple right censoring to be present in the data. This type of filtering is omnipresent in biostatistical and demographical applications, where people can join a study, leave the study and perhaps join the study again. The estimation methodology is based on a recent class of local linear density estimators. A new stable bandwidth-selector is developed for these estimators. A data application to aggregated national mortality data is provided, where immigrations to and from the country correspond to respectively left truncation and right censoring. The aggregated mortality data study illustrates that the new practical density estimators provide an important extra element in the visual toolbox for understanding survival data.

Suggested Citation

  • Gámiz Pérez, M. Luz & Martínez Miranda, María Dolores & Nielsen, Jens Perch, 2013. "Smoothing survival densities in practice," Computational Statistics & Data Analysis, Elsevier, vol. 58(C), pages 368-382.
  • Handle: RePEc:eee:csdana:v:58:y:2013:i:c:p:368-382
    DOI: 10.1016/j.csda.2012.09.011
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    References listed on IDEAS

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    1. repec:eee:csdana:v:56:y:2012:i:12:p:4011-4025 is not listed on IDEAS
    2. Hart, Jeffrey D. & Lee, Cherng-Luen, 2005. "Robustness of one-sided cross-validation to autocorrelation," Journal of Multivariate Analysis, Elsevier, vol. 92(1), pages 77-96, January.
    3. Mammen, Enno & Martínez Miranda, María Dolores & Nielsen, Jens Perch & Sperlich, Stefan, 2011. "Do-Validation for Kernel Density Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 651-660.
    4. Savchuk, Olga Y. & Hart, Jeffrey D. & Sheather, Simon J., 2010. "Indirect Cross-Validation for Density Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 105(489), pages 415-423.
    5. Dimitrios Bagkavos, 2011. "Local linear hazard rate estimation and bandwidth selection," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 63(5), pages 1019-1046, October.
    6. Tine Buch-Kromann & Jens Nielsen, 2012. "Multivariate density estimation using dimension reducing information and tail flattening transformations for truncated or censored data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(1), pages 167-192, February.
    7. Buch-Kromann, Tine & Guillén, Montserrat & Linton, Oliver & Nielsen, Jens Perch, 2011. "Multivariate density estimation using dimension reducing information and tail flattening transformations," Insurance: Mathematics and Economics, Elsevier, vol. 48(1), pages 99-110, January.
    8. Balakrishnan, N. & Kundu, Debasis, 2013. "Hybrid censoring: Models, inferential results and applications," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 166-209.
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