Abstract：
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 [J. R. Stat. Soc. Ser. B. Stat. Methodol., 63 (2001), pp. 425-464] 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.
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ASA Journal on Uncertainty Quantification
Year： 2020
Issue： 4
Volume： 8
Page： 1522-1547
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ESI Highly Cited Papers on the List： 0 Unfold All
WanFang Cited Count： -1
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30 Days PV： 8
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