Semiparametric methods of hypothesis testing about average value on basis of decomposition in space of Kunchenko

The new method of statistical hypothesis test about the mean value of random values, being based on the decomposition in space with a generative element (Kunchenko´s space) and use the property of the minimization of the variance of stochastic polynomials is offered. Gained analytical expressions allow optimizing deciding rules on a certain high-quality criterion and expecting the probabilities of errors during solution of problem. The comparing of the polynomial of deciding rules during to linear rule is conducted by a statistical design.