Robust designs for models with possible bias and correlated errors  

作　　者：ZHOU Xiao-dong YUE Rong-xian 

机构地区：[1]Department of Mathematics, Shanghai Normal University, Shanghai 200234, China [2]Business Information Management School, Shanghai Institute of Foreign Trade, Shanghai 201620 China.

出　　处：《Applied Mathematics(A Journal of Chinese Universities)》2010年第3期307-317,共11页高校应用数学学报（英文版）（B辑）

基　　金：Supported by NSFC grant(10671129);the Special Funds for Doctoral Authorities of Education Ministry(20060270002);E-Institutes of Shanghai Municipal Education Commission(E03004);Shanghai Leading Academic Discipline Project(S30405)

摘　　要：This paper studies the model-robust design problem for general models with an unknown bias or contamination and the correlated errors. The true response function is assumed to be from a reproducing kernel Hilbert space and the errors are fitted by the qth order moving average process MA（q）, especially the MA（1） errors and the MA（2） errors. In both situations, design criteria are derived in terms of the average expected quadratic loss for the least squares estimation by using a minimax method. A case is studied and the orthogonality of the criteria is proved for this special response. The robustness of the design criteria is discussed through several numerical examples.This paper studies the model-robust design problem for general models with an unknown bias or contamination and the correlated errors. The true response function is assumed to be from a reproducing kernel Hilbert space and the errors are fitted by the qth order moving average process MA（q）, especially the MA（1） errors and the MA（2） errors. In both situations, design criteria are derived in terms of the average expected quadratic loss for the least squares estimation by using a minimax method. A case is studied and the orthogonality of the criteria is proved for this special response. The robustness of the design criteria is discussed through several numerical examples.

关 键 词：Robust design reproducing kernel Hilbert space moving average process Hermite polynomial. 

分 类 号：O211.9[理学—概率论与数理统计] TN966[理学—数学]