多响应近似线性回归模型的Minmax稳健设计

研究多响应变量近似线性回归模型的Minmax稳健设计问题．以响应变量均方误差阵的迹tr（MSEM）为准则，对回归方程系数采用广义最小二乘估计，进而利用最小二乘法得到最优逼近函数．从而将Huber（1975）的方法和Wiens（1990）的结果推广到多响应变量场合．最后考察了一个特例，即当回归变量问可能存在交互作用时的双响应二元曲面线性回归模型，得到了与Wiens（1990）较一致的结果．

Robust minimax designs for multiresponse linear regression

We establish an extension, in the case of multiresponse regression, of a result on minimax multiple regression designs due to D. P. Wiens(1990) . A design is found which is minimax with respect to the trace of the integrated mean squared error matrix as the true response function varies over an L2- neighbourhood of a bivariate surface with possible interactions between the regressors.