Kang, Lulu; Joseph, V. Roshan Kernel approximation: from regression to interpolation. (English) Zbl 1381.62063 SIAM/ASA J. Uncertain. Quantif. 4, 112-129 (2016). Summary: In this paper we introduce a new interpolation method, known as kernel interpolation (KI), for modeling the output from expensive deterministic computer experiments. We construct it by repeating a generalized version of the classic Nadaraya-Watson kernel regression an infinite number of times. Although this development is numerical, we are able to provide a statistical framework for KI using a nonstationary Gaussian process. This enables us to quantify the uncertainty in the predictions as well as estimate the unknown parameters in the model using the empirical Bayes method. Through some theoretical arguments and numerical examples, we show that KI has better prediction performance than the popular kriging method in certain situations. Cited in 3 Documents MSC: 62G08 Nonparametric regression and quantile regression 62C12 Empirical decision procedures; empirical Bayes procedures Keywords:computer experiments; Gaussian process; kernel regression; kriging Software:R; MASS (R); tgp; np; mda PDFBibTeX XMLCite \textit{L. Kang} and \textit{V. R. Joseph}, SIAM/ASA J. Uncertain. Quantif. 4, 112--129 (2016; Zbl 1381.62063) Full Text: DOI Link References: [1] W. S. Cleveland, {\it Robust locally weighted regression and smoothing scatterplots}, J. Amer. Statist. Assoc., 74 (1979), pp. 829-836. · Zbl 0423.62029 [2] J. Fan and I. Gijbels, {\it Local Polynomial Modelling and Its Applications}, Chapman & Hall, London, 1996. · Zbl 0873.62037 [3] K.-T. Fang, R. Li, and A. Sudjianto, {\it Design and Modeling for Computer Experiments}, Chapman & Hall/CRC, Boca Raton, FL, 2006. · Zbl 1093.62117 [4] G. E. Fasshauer and J. G. Zhang, {\it Iterated approximate moving least squares approximation}, in Advances in Meshfree Techniques, V. M. A. 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