计算机仿真模型广泛应用于工业工程等领域, 借助真实的物理观测对计算机模型的校准参数进行估计, 可以提高计算机模型的仿真精度. 已有文献 指出, 当物理试验的试验点独立同分布于均匀分布时, 计算机模型校准参 数的$L_2$估计半参数有效. 然而真实的物理试验点往往不满足独立同分布于 均匀分布这一条件, 文章证明了在固定的试验点下, 较准参数$L_2$估计的相合性和渐近正态性, 并通过数值模拟验证了$L_2$估计的收敛速度.

Computer simulations are widely used in engineering. The input values of the model parameters can significantly affect the accuracy of the computer outputs. When physical observations are available, one can adjust the computer model parameters so that the computer outputs match the physical data. The existing results show that when the physical samples are i.i.d. and subject to uniform distribution, the $L_2$ calibration is semi-parametric efficiency. However, most designs are not i.i.d., thus, we give the convergence properties of $L_2$ calibration under fixed designs. The convergence rate of $L_2$ calibration is further verified by two numerical examples.