A problem of hypothesis testing is considered for a model of diffusion process with diffusion coefficient tending to zero. A simple hypothesis and a semiparametric alternative are formulated in the terms of the values of some functional of nonperturbed trajectory of the dynamical system. The...

The aim of this paper is to show a simple way to construct a symptotic minimax lower bounds for risks based on different types of quadratic loss functions in semiparametric inference problems. For the sake of clarity, we consider the simple case of the state estimation of a dynamical system with...

In this paper we consider a class of nonparametric estimators of a distribution function F, with compact support, based on the theory of IFSs. The estimator of F is tought as the fixed point of a contractiv eoperator T defined in terms of a vector of parameters p and a family of affine maps W...