# Geometrical aspects of testing the complex statistical hypotheses in mathematical simulation

Category «Mathematics»

## Abstract

It is well known that mathematical simulation parameters often are obtained by statistical estimating. Therefore the problem of testing the complex statistical hypotheses such as the one about an adjunct of a vector of model parameters to some domain is of current concern. This article deals with the problem in geometrical aspects. The basic theorem to solve this problem has been stated and proved. The theorem asserts that the solution can be done through testing some simple statistical hypothesis concerning a boundary point of maximum likelihood. The theorem proof is based on the use of 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 estimating; an estimation of specific enterprise is treated in terms of the statistical hypotheses testing; (ii) the method to refine statistical estimations of production function parameters; (iii) the statistical estimation of the space object dynamic stability is considered on the basis of Kepler’s model, as well.

**Keywords:**
BOUNDARY POINT OF MAXIMUM LIKELIHOOD, LAGRANGE TASK, ELLIPSOID OF RELIABILITY, GENERALIZED EUCLIDEAN METRIC

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