In this study, a variety of statistical models of regression type is considered. In some models observations are to be added by the respective design points if the latter are observable. Our models contain discontinuities of the response functions. In the case of a one-dimensional factor - an input variable - these discontinuities are presented by some change points. In the multivariate factor models, the discontinuities become functions. In either case, the principal objective of the statistical estimation is this discontinuity, a point or a function. Another feature of our models is that...