论文标题
具有高频数据的多维扩散模型中的非参数贝叶斯估计
Nonparametric Bayesian estimation in a multidimensional diffusion model with high frequency data
论文作者
论文摘要
我们认为在多维扩散模型中，非参数贝叶斯推断，基于离散的高频观测，反映边界条件。我们证明了$ l^2 $ -loss中的一般后验收缩率定理，该定理适用于高斯先生。结果的后代及其后手段被证明在任何维度上都以最小的hölder平滑度类别以最小的最佳速率收敛到地面真理。在我们的证据中，我们表明某些经常惩罚的最小二乘估计量也是最小的。
We consider nonparametric Bayesian inference in a multidimensional diffusion model with reflecting boundary conditions based on discrete high-frequency observations. We prove a general posterior contraction rate theorem in $L^2$-loss, which is applied to Gaussian priors. The resulting posteriors, as well as their posterior means, are shown to converge to the ground truth at the minimax optimal rate over Hölder smoothness classes in any dimension. Of independent interest and as part of our proofs, we show that certain frequentist penalized least squares estimators are also minimax optimal.
