The paper considers an approach to the construction and study of the emission (volt-ampere) characteristics of a system with a field electron cathode by regression analysis methods. A three-parameter model of the field electron emission signal is proposed. Estimates of the parameters of the current dependence on voltage are obtained in the framework of mathematical modeling. Estimation is carried out using a quadratic functional for linear and nonlinear models. Model selection should be determined by the analysis of so-called “regression residuals”, which are influenced by measurement errors. The validity of the application of both the linear and weighted nonlinear least-squares methods is shown as a result of mathematical modeling.