The approach to constructing and investigating of emission (current-voltage) characteristics for a system with a field electron cathode by regression analysis methods is considered. The three-parameter model of the field electron emission signal is proposed. The parameters estimations of the current-voltage dependence are obtained in terms of mathematical modeling. The estimation is carried out with the quadratic functional for the linear and nonlinear models. The model selection should be conditioned by the analysis of the so-called regression residuals, the influence of which is affected by measurement errors. As a result of mathematical modeling, a good work of both a linear method and a weighted non-linear least-squares method is demonstrated.