R. de Jonge
H. van Zanten
- Semiparametric Bernstein-von Mises for the error standard deviation
- Electronic Journal of Statistics
- Pages (from-to)
- Document type
- Faculty of Science (FNWI)
- Korteweg-de Vries Institute for Mathematics (KdVI)
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−√-consistent estimation of the error standard deviation.
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