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...

Reliability of products is often determined by special technical or physical drift parameters. Suitable stochastic processes are applied to model such drift processes. An failure can be observed when the drift process leaves a given region at the first time. Then the lifetime is the random time...

Reliability of products is often determined by special technical or physical drift parameters. Suitable stochastic processes are applied to model such drift processes. An failure can be observed when the drift process leaves a given region at the first time. Then the lifetime is the random time...

We consider the properties of the maximum likelihood, Bayes and minimum distance estimates of the finite-dimensional parameter constructed by the observations of the process of diffusion type with the small coefficient of diffusion in the situation when the trend coefficients corresponding to...