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 contractive operator T defined in terms of a vector of parameters p and a family of affine maps W...

In this small note an iterated function system on the space of distribution functions is built. The inverse problem is introduced and studied by convex optimization problems. Applications of this method to approximation of distribution functions and estimations are presented

In this paper we review some recent results concerning the approximations of distribution functions and measures on [0,1] based on iterated function systems. The two different approaches available in the literature are considered and their relation are investigated in the statistical...

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...

The aim of this paper is to show a simple way to construct asymptotic 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...

A subthreshold signal is transmitted through a channel and may be detected when some noise { with known structure and proportional to some level { is added to the data. There is an optimal noise level, called stochastic resonance, that corresponds to the highest Fisher information in the problem...

A problem of hypothesis testing is considered for a model of diffusion process with diusion coecient 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 test...