AStA Advances in Statistical Analysis

, Volume 97, Issue 1, pp 33–47 | Cite as

Nearest neighbor hazard estimation with left-truncated duration data

  • Rafael WeißbachEmail author
  • Wladislaw Poniatowski
  • Walter Krämer
Original Paper


Duration data often suffer from both left-truncation and right-censoring. We show how both deficiencies can be overcome at the same time when estimating the hazard rate nonparametrically by kernel smoothing with the nearest-neighbor bandwidth. Smoothing Turnbull’s estimator of the cumulative hazard rate, we derive strong uniform consistency of the estimate from Hoeffding’s inequality, applied to a generalized empirical distribution function. We also apply our estimator to rating transitions of corporate loans in Germany.


Kernel smoothing Hazard rate Left-truncation Right-censoring 



Financial support by Deutsche Forschungsgemeinschaft is gratefully acknowledged (SFB 823 and Grant WE3573/2).


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Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  • Rafael Weißbach
    • 1
    Email author
  • Wladislaw Poniatowski
    • 2
  • Walter Krämer
    • 3
  1. 1.Lehrstuhl Statistik, Institut für Volkswirtschaftslehre, Fakultät für Wirtschafts- und SozialwissenschaftenUniversität RostockRostockGermany
  2. 2.Deutsche TelekomBonnGermany
  3. 3.Fakultät StatistikTechnische Universität DortmundDortmundGermany

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