On the Improved Rates of Convergence for Matern-Type Kernel Ridge Regression with Application to Calibration of Computer Models Academic Article

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 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.

authors

• Tuo, Rui

published proceedings

• SIAM-ASA JOURNAL ON UNCERTAINTY QUANTIFICATION

author list (cited authors)

• Tuo, R., Wang, Y., & Wu, C.

citation count

• 11

complete list of authors

• Tuo, Rui||Wang, Yan||Wu, CF Jeff

publication date

• January 2020

publisher

• Society for Industrial & Applied Mathematics (SIAM)  Publisher

published in

• SIAM/ASA Journal on Uncertainty Quantification  Journal

keywords

• Calibration Of Parameters
• Kriging
• Nonparametric Regression
• Reproducing Kernel Hilbert Space

Digital Object Identifier (DOI)

• 10.1137/19M1304222

start page

• 1522

end page

• 1547

volume

• 8

issue

• 4

URL

• http://dx.doi.org/10.1137/19m1304222