Kriging Model Averaging Based on Leave-One-Out Cross-Validation Method  

作　　者：FENG Ziheng ZONG Xianpeng XIE Tianfa ZHANG Xinyu 

机构地区：[1]School of Mathematics,Statistics and Mechanics,Beijing University of Technology,Beijing 100124,China [2]Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China

出　　处：《Journal of Systems Science & Complexity》2024年第5期2132-2156,共25页系统科学与复杂性学报（英文版）

基　　金：supported by the National Natural Science Foundation of China under Grant Nos.71973116 and 12201018;the Postdoctoral Project in China under Grant No.2022M720336;the National Natural Science Foundation of China under Grant Nos.12071457 and 11971045;the Beijing Natural Science Foundation under Grant No.1222002;the NQI Project under Grant No.2022YFF0609903。

摘　　要：In recent years,Kriging model has gained wide popularity in various fields such as space geology,econometrics,and computer experiments.As a result,research on this model has proliferated.In this paper,the authors propose a model averaging estimation based on the best linear unbiased prediction of Kriging model and the leave-one-out cross-validation method,with consideration for the model uncertainty.The authors present a weight selection criterion for the model averaging estimation and provide two theoretical justifications for the proposed method.First,the estimated weight based on the proposed criterion is asymptotically optimal in achieving the lowest possible prediction risk.Second,the proposed method asymptotically assigns all weights to the correctly specified models when the candidate model set includes these models.The effectiveness of the proposed method is verified through numerical analyses.

关 键 词：Asymptotic optimality best linear unbiased prediction cross-validation Kriging model model averaging 

分 类 号：O212[理学—概率论与数理统计]