Abstract

We consider a two-parameter regression model based on the Fowler–Nordheim equation, which is classical for the field of field electron emission. The optimal parameter values are determined by the least-squares method. The characteristics of the confidence intervals are evaluated as part of a statistical experiment. We pay attention to the accuracy of estimates, the boundaries of individual confidence intervals, and joint confidence ellipses. Two types of experimental designs are used for the voltage values. The error in the current measurements is generated using a special noise model. During the computer experiment, the data are subjected to the Shapiro–Wilk test, which verifies the normality of their distribution, and the regression model is tested for significance. The percentage of samples that may not meet the specified criteria is revealed.

中文翻译：

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基于Fowler-Nordheim定律的回归模型参数的置信区间分析

摘要

我们考虑基于Fowler-Nordheim方程的两参数回归模型，这是场电子发射领域的经典模型。最佳参数值由最小二乘法确定。置信区间的特征将作为统计实验的一部分进行评估。我们注意估计的准确性，单个置信区间的边界以及联合置信椭圆。电压值使用两种类型的实验设计。当前测量中的误差是使用特殊的噪声模型生成的。在计算机实验期间，对数据进行Shapiro-Wilk检验，以验证其分布的正态性，并测试回归模型的重要性。显示了可能不符合指定标准的样品百分比。