Supremum norm posterior contraction and credible sets for nonparametric multivariate regression
多元非参数回归的上确界范数后验收缩与可信集
In the setting of nonparametric multivariate regression with unknown error variance $\sigma^{2}$, we study asymptotic properties of a Bayesian method for estimating a regression function $f$ and its mixed partial derivatives. We use a random series of tensor product of B-splines with normal basis coefficients as a prior for $f$, and $\sigma$ is either estimated using the empirical Bayes approach or is endowed with a suitable prior in a hierarchical Bayes approach. We…