Kriging Prediction with Isotropic Matern Correlations: Robustness and Experimental Designs
Kriging Prediction with Isotropic Matern Correlations: Robustness and Experimental Designs
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发表时间：
2019-11
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通讯作者：
Rui Tuo;Wenjia Wang
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作者：
Rui Tuo;Wenjia Wang
我们调查的克里金预测器的预测性能。当真实相关函数和附加相关函数的谱密度都是代数衰减时，在一致度量和L_p度量下，我们得到了预测误差的非渐近误差界. Matern家族是这类相关函数的一个突出的类别。我们发现，当施加的相关函数的平滑度超过真正的相关函数，预测误差变得更加敏感的设计点的空间填充属性。特别地，我们证明了，上述克里金预测仍然可以达到最佳的收敛速度，如果实验设计方案是准均匀的。我们还得到了一致度量和$L_p$度量下的克立格预测误差的下界。当使用过平滑相关函数和空间填充设计时，获得了此误差的准确表征。
We investigate the prediction performance of the kriging predictors. We derive some non-asymptotic error bounds for the prediction error under the uniform metric and $L_p$ metrics when the spectral densities of both the true and the imposed correlation functions decay algebraically. The Matern family is a prominent class of correlation functions of this kind. We show that, when the smoothness of the imposed correlation function exceeds that of the true correlation function, the prediction error becomes more sensitive to the space-filling property of the design points. In particular, we prove that, the above kriging predictor can still reach the optimal rate of convergence, if the experimental design scheme is quasi-uniform. We also derive a lower bound of the kriging prediction error under the uniform metric and $L_p$ metrics. An accurate characterization of this error is obtained, when an oversmoothed correlation function and a space-filling design is used.