Translator Disclaimer
2012 Adaptive estimation of multivariate functions using conditionally Gaussian tensor-product spline priors
R. de Jonge, J.H. van Zanten
Electron. J. Statist. 6(none): 1984-2001 (2012). DOI: 10.1214/12-EJS735

Abstract

We investigate posterior contraction rates for priors on multivariate functions that are constructed using tensor-product B-spline expansions. We prove that using a hierarchical prior with an appropriate prior distribution on the partition size and Gaussian prior weights on the B-spline coefficients, procedures can be obtained that adapt to the degree of smoothness of the unknown function up to the order of the splines that are used. We take a unified approach including important nonparametric statistical settings like density estimation, regression, and classification.

Citation

Download Citation

R. de Jonge. J.H. van Zanten. "Adaptive estimation of multivariate functions using conditionally Gaussian tensor-product spline priors." Electron. J. Statist. 6 1984 - 2001, 2012. https://doi.org/10.1214/12-EJS735

Information

Published: 2012
First available in Project Euclid: 30 October 2012

zbMATH: 1295.62007
MathSciNet: MR3020254
Digital Object Identifier: 10.1214/12-EJS735

Subjects:
Primary: 62C10
Secondary: 62G20

Rights: Copyright © 2012 The Institute of Mathematical Statistics and the Bernoulli Society

JOURNAL ARTICLE
18 PAGES


SHARE
Back to Top