On the Improved Rates of Convergence for Matérn-Type Kernel Ridge Regression with Application to Calibration of Computer Models
On the Improved Rates of Convergence for Matérn-Type Kernel Ridge Regression with Application to Calibration of Computer Models
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DOI：
10.1137/19m1304222
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发表时间：
2020-01
期刊：
影响因子：
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通讯作者：
Rui Tuo;Yan Wang;C. F. Wu
中科院分区：
文献类型：
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作者：
Rui Tuo;Yan Wang;C. F. Wu
核脊回归是光滑函数估计的一种重要的非参数方法。我们引入了核脊回归估计量在L_2范数和再现核希尔伯特空间范数下的实际收敛速率超过标准极大极小速率的一组新的条件。这一理论的应用导致了对Kennedy-O'Hagan方法校准计算机模拟模型参数的新理解。证明了在一定条件下，具有已知协方差函数的Kennedy-O'Hagan校准估计量收敛于再现核Hilbert空间中残差函数范数的极小值。
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.