This paper investigates the role of the augmentation parameter in the Finite Selection Model (FSM) and its impact on estimator performance. Through a comprehensive Monte Carlo simulation study, we analyze the sensitivity of bias, variance, and mean squared error to different values of the augmentation parameter. The results demonstrate that moderate augmentation improves covariate balance while maintaining estimation efficiency. However, excessive augmentation may increase variance and reduce estimator stability. The findings provide practical guidelines for selecting the augmentation parameter in applied experimental design settings.

翻译：本文研究了有限选择模型（FSM）中增强参数的作用及其对估计量性能的影响。通过全面的蒙特卡洛模拟研究，我们分析了偏差、方差和均方误差对不同增强参数值的敏感性。结果表明，适度的增强在保持估计效率的同时改善了协变量平衡。然而，过度的增强可能会增加方差并降低估计量的稳定性。这些发现为应用实验设计场景中选择增强参数提供了实用指导。