One of the differences between the regression models using the function representation of 3-layered neural network and the traditional linear regression models is whether the nonlinear parameters associated with the basis functions exist or not, where these parameters play a role of varying the form of the basis so as to minimize the square error. In this study, we gave attention to this feature and defined the regression model using the function representation with step-type discrete variable basis. Then we obtained the bounds of the asymptotic expectations of the least square error and the prediction square error with respect to the sample distribution using the extreme value theory. These results will provide an effective approach to the statistical properties of 3-layered neural network.