We propose a method of adaptive estimation of a regression function and which is near optimal in the classical sense of the mean integrated error. At the same time, the estimator is shown to be very sensitive to discontinuities or change-points of the underlying function f or its derivatives....

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...

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 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...

Let a process SI , ... ,ST obey the conditionally heteroskedastic equation St = Vt Et whcrc Et is a random noise and Vt is the volatility coefficient which in turn obeys an autoregression type equation log v t = w + a S t- l + nt with an additional noise nt. We consider the situation which the...

Suppose that one observes a process Y on the unit interval, where dY(t) = n 1/ 2f(t)dt + dW(t) with an unknown function parameter f, given scale parameter n N 1 ("sample size") and standard Brownian motion W. We propose two classes of tests of qualitative nonparametric hypotheses about f such...

Price variations observed at speculative markets exhibit positive autocorrelation and cross correlation among a set of assets, stock market indices, exchange rates etc. A particular problem in investigating multivariate volatility processes arises from the high dimensionality implied by a...