Estimating relative risk on the line using nearest neighbor statistics

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This paper considers a non-parametric method for identifying intervals on the line where the relative risk of cases to controls exceeds a pre-specified level. The method is based on the k th nearest neighbor (kNN) approach for density estimation. An asymptotic result is presented that yields an explicit formula for constructing a confidence interval for the relative risk at a given point. Numerical simulations are used to compare this approach with a kernel density estimation procedure. An application is made to a case-control study in which the relative risk of motor vehicle crashes caused by female drivers is compared to male drivers in the state of Kentucky as a function of age and then by time of day.

Original languageEnglish
Pages (from-to)249-265
Number of pages17
JournalMethodology and Computing in Applied Probability
Issue number2 SPEC. ISS.
StatePublished - Jun 2009

Bibliographical note

Funding Information:
Acknowledgements The collision data were provided by Dr. Terry Bunn (Kentucky Injury Prevention and Research Center, University of Kentucky). This work was partially supported by Grant/Cooperative Agreement Number 1U60OH008483-01 from The National Institute for Occupational Safety and Health (NIOSH). Its contents are solely the responsibility of the authors and do not necessarily represent the official views of NIOSH.


  • Incomplete beta approximation
  • Motor vehicle crashes
  • Permutation tests
  • Relative risk function
  • kNN density estimator

ASJC Scopus subject areas

  • Statistics and Probability
  • Mathematics (all)


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