How to improve accuracy of estimation

The new approach, allowed to take into account some additional information, coming from datas, is proposed. The main idea is to obtain from datas some information about structure of the model in order to improve accuracy of estimation. It seems to be important, since standard nonparametric accuracy of estimation is usually very low. To improve one statisticians often impose some additional structure on considerable model, that can lead to inadequate model. To avoid both these disadvantages special form of estimation procedure, based on some combination of adaptive technique and hypothesis testing, is applied. From mathematical point of view it leads to the consideration of new kind of minimax risks. From practical point of view it allows to improve accuracy of estimation procedures even for the cases when guess on special structure of a model turns out to be wrong.