Geometrical aspects of testing complex statistical hypotheses in mathematical simulation

It is well known that mathematical simulation parameters are often obtained by statistical estimation. Therefore the problem of testing complex statistical hypotheses, such as the one about a model parameters vector belonging to some domain, is of current concern. This article deals with the geometrical aspects of the problem. The basic theorem to solve this problem has been stated and proved. The theorem asserts that the solution can be obtained through testing some simple statistical hypothesis concerning a boundary point of maximum likelihood. The theorem proof is based on the use of a generalized Euclidean metric and an affine transformation of parameter space. Typical examples of its use for different mathematical models are also considered. They are the following: (i) Altman's model of the economic stability and risk assessment; an assessment of a specific enterprise is treated in terms of statistical hypotheses testing; (ii) a method to refine statistical estimations of production function parameters; (iii) a statistical estimation of spacecraft dynamic stability is considered on the basis of Kepler's model, as well.