论文标题
关于Matérn型内核山脊回归的收敛速度的提高，并应用了计算机模型的校准
On the Improved Rates of Convergence for Matérn-type Kernel Ridge Regression, with Application to Calibration of Computer Models
论文作者
论文摘要
内核脊回归是一种重要的非参数方法，用于估计平滑功能。我们介绍了一套新的条件，根据该条件，在L_2 Norm和繁殖核Hilbert Space的实际收敛速率下，核脊回归估计器都超过了标准的最小值速率。该理论的应用导致对肯尼迪 - 奥哈根（Kennedy-O'Hagan）方法的新理解，用于校准计算机模拟的模型参数。我们证明，在某些条件下，具有已知协方差函数的Kennedy-O'Hagan校准估计量会收敛到繁殖核Hilbert空间中残留函数规范的最小化器。
Kernel ridge regression is an important nonparametric method for estimating smooth functions. We introduce a new set of conditions, under which the actual rates of convergence of the kernel ridge regression estimator under both the L_2 norm and the norm of the reproducing kernel Hilbert space exceed the standard minimax rates. An application of this theory leads to a new understanding of the Kennedy-O'Hagan approach for calibrating model parameters of computer simulation. We prove that, under certain conditions, the Kennedy-O'Hagan calibration estimator with a known covariance function converges to the minimizer of the norm of the residual function in the reproducing kernel Hilbert space.
