Fiducial Theory for Free-Knot Splines

Conference paper

DOI: 10.1007/978-3-319-02651-0_10

Volume 68 of the book series Springer Proceedings in Mathematics & Statistics (PROMS)
Cite this paper as:
Sonderegger D., Hannig J. (2014) Fiducial Theory for Free-Knot Splines. In: Lahiri S., Schick A., SenGupta A., Sriram T. (eds) Contemporary Developments in Statistical Theory. Springer Proceedings in Mathematics & Statistics, vol 68. Springer, Cham

Abstract

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.

Keywords

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

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