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.
Original language | English |
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Pages (from-to) | 1984-2001 |
Journal | Electronic Journal of Statistics |
Volume | 6 |
DOIs | |
Publication status | Published - 2012 |