Bayesian local extremum splines

Journal Article

We consider shape-restricted nonparametric regression on a closed set $$\mathcal{X} \subset \mathbb{R},$$ where it is reasonable to assume that the function has no more than $$H$$ local extrema interior to $$\mathcal{X}$$. Following a Bayesian approach we develop a nonparametric prior over a novel class of local extremum splines. This approach is shown to be consistent when modelling any continuously differentiable function within the class considered, and we use itto develop methods for testing hypotheses on the shape of the curve. Sampling algorithms are developed, and the method is applied in simulation studies and data examples where the shape of the curve is of interest.

Full Text

Duke Authors

Cited Authors

  • Wheeler, MW; Dunson, DB; Herring, AH

Published Date

  • December 1, 2017

Published In

Volume / Issue

  • 104 / 4

Start / End Page

  • 939 - 952

PubMed ID

  • 29422695

Pubmed Central ID

  • PMC5798493

International Standard Serial Number (ISSN)

  • 0006-3444

Digital Object Identifier (DOI)

  • 10.1093/biomet/asx039