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Boundary and Bias Correction in Kernel Hazard Estimation

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  • Jens Perch Nielsen
  • Carsten Tanggaard

Abstract

A new class of local linear hazard estimators based on weighted least square kernel estimation is considered. The class includes the kernel hazard estimator of Ramlau‐Hansen (1983), which has the same boundary correction property as the local linear regression estimator (see Fan & Gijbels, 1996). It is shown that all the local linear estimators in the class have the same pointwise asymptotic properties. We derive the multiplicative bias correction of the local linear estimator. In addition we propose a new bias correction technique based on bootstrap estimation of additive bias. This latter method has excellent theoretical properties. Based on an extensive simulation study where we compare the performance of competing estimators, we also recommend the use of the additive bias correction in applied work.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:scjsta:v:28:y:2001:i:4:p:675-698
    DOI: 10.1111/1467-9469.00262
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    Cited by:

    1. Gerard J. van den Berg & Antoine Bozio & Mónica Costa Dias, 2020. "Policy discontinuity and duration outcomes," Quantitative Economics, Econometric Society, vol. 11(3), pages 871-916, July.
    2. Stephan M. Bischofberger, 2020. "In-Sample Hazard Forecasting Based on Survival Models with Operational Time," Risks, MDPI, vol. 8(1), pages 1-17, January.
    3. Jens Perch Nielsen & Carsten Tanggaard & M.C. Jones, 2007. "Local Linear Density Estimation for Filtered Survival Data, with Bias Correction," CREATES Research Papers 2007-13, Department of Economics and Business Economics, Aarhus University.
    4. María Luz Gámiz & Enno Mammen & María Dolores Martínez Miranda & Jens Perch Nielsen, 2016. "Double one-sided cross-validation of local linear hazards," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(4), pages 755-779, September.
    5. Fernandes, Marcelo & Grammig, Joachim, 2005. "Nonparametric specification tests for conditional duration models," Journal of Econometrics, Elsevier, vol. 127(1), pages 35-68, July.
    6. Feng Chen & Richard M. Huggins & Paul S. F. Yip & K. F. Lam, 2008. "Local polynomial estimation of Poisson intensities in the presence of reporting delays," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 57(4), pages 447-459, September.
    7. Janys, Lena, 2017. "A General Semiparametric Approach to Inference with Marker-Dependent Hazard Rate Models," VfS Annual Conference 2017 (Vienna): Alternative Structures for Money and Banking 168077, Verein für Socialpolitik / German Economic Association.
    8. Hirukawa, Masayuki, 2010. "Nonparametric multiplicative bias correction for kernel-type density estimation on the unit interval," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 473-495, February.
    9. 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.
    10. Bischofberger, Stephan M. & Hiabu, Munir & Mammen, Enno & Nielsen, Jens Perch, 2019. "A comparison of in-sample forecasting methods," Computational Statistics & Data Analysis, Elsevier, vol. 137(C), pages 133-154.
    11. van den Berg, Gerard J. & Janys, Lena & Mammen, Enno & Nielsen, Jens P., 2014. "A General Semiparametric Approach to Inference with Marker-Dependent Hazard Rate Models," IZA Discussion Papers 8339, Institute of Labor Economics (IZA).
    12. Wolter, James Lewis, 2016. "Kernel estimation of hazard functions when observations have dependent and common covariates," Journal of Econometrics, Elsevier, vol. 193(1), pages 1-16.
    13. van den Berg, Gerard. J. & Janys, Lena & Mammen, Enno & Nielsen, Jens Perch, 2021. "A general semiparametric approach to inference with marker-dependent hazard rate models," Journal of Econometrics, Elsevier, vol. 221(1), pages 43-67.
    14. Gámiz, María Luz & Mammen, Enno & Martínez-Miranda, María Dolores & Nielsen, Jens Perch, 2022. "Missing link survival analysis with applications to available pandemic data," Computational Statistics & Data Analysis, Elsevier, vol. 169(C).
    15. 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.
    16. Wenzhuan Zhang & Yingcun Xia, 2012. "Twicing local linear kernel regression smoothers," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(2), pages 399-417.
    17. 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.
    18. Gámiz, Maria Luz & Lindqvist, Bo Henry, 2016. "Nonparametric estimation in trend-renewal processes," Reliability Engineering and System Safety, Elsevier, vol. 145(C), pages 38-46.
    19. James Wolter, 2015. "Kernel Estimation Of Hazard Functions When Observations Have Dependent and Common Covariates," Economics Series Working Papers 761, University of Oxford, Department of Economics.
    20. Spierdijk, Laura, 2008. "Nonparametric conditional hazard rate estimation: A local linear approach," Computational Statistics & Data Analysis, Elsevier, vol. 52(5), pages 2419-2434, January.

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