Analysis of Confidence Intervals for Regression Model Parameters, Based on the Fowler-Nordheim Law

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.