The paper is concerned with the problem of image denoising for the case of grey-scale images. Such images consist of a finite number of regions with smooth boundaries and the image value is assumed piecewise constant within each region. New method of image denoising is proposed which is adaptive...

We consider a two-scaled diffusion system, when drift and diffusion parameters of the “slow” component are contaminated by the "fast" unobserved component. The goal is to estimate the dynamic function which is defined by averaging the drift coefficient of the "slow" component w.r.t. the...

We develop a new test of a parametric model of a conditional mean function against a nonparametric alternative. The test adapts to the unknown smoothness of the alternative model and is uniformly consistent against alternatives whose distance from the parametric model converges to zero at the...

The paper is concerned with the problem of variance estimation for a high-dimensional regression model. The results show that the accuracy n -1/2 of variance estimation can be achieved only under some restrictions on smoothness properties of the regression function and on the dimensionality of...

This paper offers a new approach for estimation and forecasting of the volatility of financial time series. No assumption is made about the parametric form of the processes, on the contrary we only suppose that the volatility can be approximated by a constant over some interval. In such a...

We consider the component analysis problem for a regression model with an additive structure. The problem is to check the hypothesis of linearity for each component without specifying the structure of the remaining components. In this paper we show that under mild conditions on the design and...

Sparse non-Gaussian component analysis (SNGCA) is an unsupervised method of extracting a linear structure from a high dimensional data based on estimating a low-dimensional non-Gaussian data component. In this paper we discuss a new approach to direct estimation of the projector on the target...

The paper focuses on the problem of pricing and hedging a European contingent claim for an incomplete market model, in which evolution of price processes for a saving account and stocks depends on an observable Markov chain. The pricing function is evaluated using the martingale approach. The...

Given a random sample from some unknown density fo : R → [0, ∞) we devise Haar wavelet estimators for fo with variable resolution levels constructed from localised test procedures (as in Lepski, Mammen, and Spokoiny (1997, Ann. Statist.)). We show that these estimators adapt to spatially...