Robust Designs Based on the Infinitesimal Approach
提出一种无穷小方法构造线性模型的稳健设计，能抵抗响应函数微小偏离和误差相关假设微小偏离，在满足稳健约束下最小化理想模型下最小二乘估计的均方误差矩阵行列式。
Abstract We introduce an infinitesimal approach to the construction of robust designs for linear models. The resulting designs are robust against small departures from the assumed linear regression response and/or small departures from the assumption of uncorrelated errors. Subject to satisfying a robustness constraint, they minimize the determinant of the mean squared error matrix of the least squares estimator at the ideal model. The robustness constraint is quantified in terms of boundedness of the Gateaux derivative of this determinant, in the direction of a contaminating response function or autocorrelation structure. Specific examples are considered. If the aforementioned bounds are sufficiently large, then (permutations of) the classically optimal designs, which minimize variance alone at the ideal model, meet our robustness criteria. Otherwise, new designs are obtained.