Fiducial Theory for Free-Knot Splines

  • Derek L. Sonderegger
  • Jan Hannig
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 68)


We construct the fiducial model for free-knot splines and derive sufficient conditions to show asymptotic consistency of a multivariate fiducial estimator. We show that splines of degree four and higher satisfy those conditions and conduct a simulation study to evaluate quality of the fiducial estimates compared to the competing Bayesian solution. The fiducial confidence intervals achieve the desired confidence level while tending to be shorter than the corresponding Bayesian credible interval using the reference prior. AMS 2000 subject classifications: Primary 62F99, 62G08; secondary 62P10.


Free-knot splines Generalized fiducial inference Bernstein-von Mises theorem 



Dr Hannig thanks Prof. Hira Koul for his encouragement and help ever since he was a graduate student at Michigan State University. A young researcher cannot ask for a better role model. The authors also thank the two anonymous referees that made several useful suggestions for improving the manuscript.


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsNorthern Arizona UniveristyFlagstaffUSA
  2. 2.Department of Statistics and Operations ResearchUniversity of North CarolinaNorth CarolinaUSA

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