Minimax procedures of statistical inference with the possibility of refusal of solution taking

The article proceeds the study of the class of statistical inference procedures with the possibility of refusal of solution taking in the way which was formulated in the author's paper [8]. The author puts and solves the minimax problems of the procedure search with refusal of solution taking. The search is made to find the procedure that minimizes the supremum of probability to refuse the solution taking if the restrictions are given for the mean losses to take a solution (risk) or minimizes the risk if the restrictions are given for the probability of the refusal. The characterization is given for the rules of taking a solution which corresponds the procedures guaranteeing the given restrictions for the risk and minimizing the probability of refusal. An example of constructing the minimax procedure of two simple hypothesis discrimination with the possibility of refusal of solution taking is given.