Electronic Journal of Statistics

Adaptive estimation of multivariate functions using conditionally Gaussian tensor-product spline priors

R. de Jonge and J.H. van Zanten

Full-text: Open access

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.

Article information

Source
Electron. J. Statist. Volume 6 (2012), 1984-2001.

Dates
First available in Project Euclid: 30 October 2012

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1351603386

Digital Object Identifier
doi:10.1214/12-EJS735

Mathematical Reviews number (MathSciNet)
MR3020254

Zentralblatt MATH identifier
1295.62007

Subjects
Primary: 62C10: Bayesian problems; characterization of Bayes procedures
Secondary: 62G20: Asymptotic properties

Keywords
Nonparametric Bayes procedure tensor-product splines posterior contraction rate adaptive estimation

Citation

de Jonge, R.; van Zanten, J.H. Adaptive estimation of multivariate functions using conditionally Gaussian tensor-product spline priors. Electron. J. Statist. 6 (2012), 1984--2001. doi:10.1214/12-EJS735. https://projecteuclid.org/euclid.ejs/1351603386


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