Finding economic optimum fertilizer rate with good accuracy is essential for optimal crop yield, efficient resource utilization, and environmental well-being. However, the prevailing incomplete understanding of input-output relationships leads to imprecise crop yield response functions, such as those for winter wheat, and potentially biased fertilizer choices. From a statistical point of view, there is uncertainity with regards to which model is most suitable to estimate the economic optimum fertilizer rate. This complexity is amplified when considering site-specific nitrogen fertilization, which factors into elements like soil attributes, topography, and crop variations within a field, as opposed to uniform application. This study undertakes a comparative analysis to evaluate biases, variance, mean squared errors and confidence intervals in Economic Optimum Nitrogen Rate (EONR) estimations across different functional forms. The goal is to uncover performance discrepancies among these forms and explore potential advantages of adopting model averaging for optimizing nitrogen use in crop cultivation. The results of simulations reveal noteworthy biases when comparing diverse yield functions with the averaged model, particularly evident in the Linear-Plateau and Mitscherlich models. Moreover, analysis of empirical data indicates that confidence intervals for the averaged model overlap with the projected ranges of all functions. This implies that the averaged model could be suitable for determining EONR and effectively address the problem of model specification without focusing on one specific functional form. The effectiveness of model averaging hinges on incorporating models that well approximate the true model. However, even if the true model is not known, the average model can provide reasonable information for determining the EONR, provided that similar model specifications are considered. This has implications for modelling of yield response for various applications and can contribute to unbiased estimations of yield response.

准确地找到经济最佳施肥量对于最佳作物产量、有效资源利用和环境福祉至关重要。然而，对投入产出关系普遍不完全的理解导致作物产量响应函数不精确，例如冬小麦的产量响应函数，以及潜在的肥料选择偏差。从统计学的角度来看，哪种模型最适合估计经济最佳施肥量存在不确定性。当考虑特定地点的氮肥时，这种复杂性会被放大，它会考虑土壤属性、地形和田间作物变化等因素，而不是统一施肥。本研究进行了比较分析，以评估不同函数形式的经济最佳氮肥率 (EONR) 估计中的偏差、方差、均方误差和置信区间。目标是揭示这些形式之间的性能差异，并探索采用模型平均来优化作物种植中氮肥使用的潜在优势。在将不同的收益率函数与平均模型进行比较时，模拟结果揭示了值得注意的偏差，在线性高原模型和 Mitscherlich 模型中尤其明显。此外，经验数据分析表明平均模型的置信区间与所有函数的预测范围重叠。这意味着平均模型可以适用于确定 EONR 并有效解决模型规范问题，而无需关注一种特定的函数形式。模型平均的有效性取决于合并能够很好地逼近真实模型的模型。然而，即使真实模型未知，只要考虑类似的模型规格，平均模型也可以提供确定 EONR 的合理信息。这对于各种应用的产量响应建模具有影响，并且有助于产量响应的无偏估计。