Samenvatting
We study Bayes procedures for nonparametric regression problems with Gaussian errors, giving conditions under which a Bernstein–von Mises result holds for the marginal posterior distribution of the error standard deviation. We apply our general results to show that a single Bayes procedure using a hierarchical spline-based prior on the regression function and an independent prior on the error variance, can simultaneously achieve adaptive, rate-optimal estimation of a smooth, multivariate regression function and efficient, n-v-consistent estimation of the error standard deviation.
Originele taal-2 | Engels |
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Pagina's (van-tot) | 217-243 |
Tijdschrift | Electronic Journal of Statistics |
Volume | 7 |
Nummer van het tijdschrift | 1 |
DOI's | |
Status | Gepubliceerd - 2013 |