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

作者：de Jonge R^*; van Zanten J H

来源：Electronic Journal of Statistics, 2012, 6: 1984-2001.

DOI：10.1214/12-EJS735

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

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 upto the order of the splines that are used. We take a unified approach including important nonparametric statistical settings like density estimation, regression, and classification.

• 出版日期2012