Adaptive estimation of multivariate functions using conditionally Gaussian tensor-product spline priors
| Authors |
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| Publication date | 2012 |
| Journal | Electronic Journal of Statistics |
| Volume | Issue number | 6 (2012) |
| Pages (from-to) | 1984-2001 |
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| 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. |
| Document type | Article |
| Language | English |
| Published at | https://doi.org/10.1214/12-EJS735 |
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