基于似无关回归的多元稳健损失函数方法  

A Robust Loss Function Approach for Multi-response Optimization Based on Seemingly Unrelated Regressions

作　　者：张旭涛[1] 何桢[2] 

机构地区：[1]军事交通学院装备保障系,天津300161 [2]天津大学管理与经济学部,天津300072

出　　处：《数理统计与管理》2017年第5期802-809,共8页Journal of Applied Statistics and Management

基　　金：国家自然科学基金重点项目(71532008)

摘　　要：针对多响应参数优化问题,考虑响应间相关性和可控因子波动的影响,提出了一种基于似无关回归的多元稳健损失函数方法。首先采用似无关回归对模型拟合和过程优化中的相关参数进行估计,更有效地利用响应间相关性信息;然后利用给定点处梯度信息来估计可控因子波动对过程稳健性的影响。算例表明,当响应间存在相关性时,与最小二乘方法相比,采用似无关回归拟合的响应曲面模型精度更高;与传统质量损失函数相比,在采用相同质量成本矩阵时,采用稳健损失函数方法得到的最优解处期望质量损失更小。A robust loss function method based on seemingly unrelated regressions （SUR） is proposed for multi-response optimization problems, which takes the correlation among responses and the effect of control factors fluctuations into account. The correlations among responses are considered through employing the SUR to model fitting and process optimization. The gradient information at given points is analyzed to estimate the process robustness. The illustrated example shows that SUR produces more precise estimates of the model parameters than ordinary least squares when responses are correlated. Compared with conventional loss function, the robust loss function can lead to a smaller expected quality loss when the same cost matrix is used, indicating that a better optimal solution is found.

关 键 词：似无关回归 多响应优化 损失函数 响应相关性 稳健性 

分 类 号：O212[理学—概率论与数理统计]