Nonparametric Estimation of a Hazard Rate Function with Right Truncated Data

  • Haci AkcinEmail author
  • Xu Zhang
  • Yichuan Zhao
Part of the ICSA Book Series in Statistics book series (ICSABSS)


Left truncation and right truncation coexist in a truncated sample. Earlier researches focused on left truncation. Lagakos et al. (Biometrika 75:515–523, 1988) proposed to transform right truncated data to left truncated data and then apply the methods developed for left truncation. Interpretation of survival quantities, such as the hazard rate function, in reverse-time is not natural. Though it is most interpretable, researchers seldom use the forward-time hazard function. In this book chapter we studied the nonparametric inference for the hazard rate function with right truncated data. Kernel smoothing techniques were used to get smoothed estimates of hazard rates. Three commonly used kernels, uniform, Epanechnikov, and biweight kernels were applied on the AIDS data to illustrate the proposed methods.



This book chapter has been greatly improved following the comments of two referees. The authors appreciate referees’ insightful suggestions on the contents of this book chapter.


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© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Department of Risk Management and InsuranceGeorgia State UniversityAtlantaUSA
  2. 2.Center for Clinical and Translational SciencesUniversity of Texas Health Science CenterHoustonUSA
  3. 3.Department of Mathematics and StatisticsGeorgia State UniversityAtlantaUSA

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