In the work a characterization of difference of multivariate Gaussian measures is found on the family of centered Eucledian balls. In particular, it helps to derive (xx see paper).

We consider a problem of multiclass classification, where the training sample Sn = {(Xi, Yi)}n i=1 is generated from the model P(Y = m

In this work, we propose to define Gaussian Processes indexed by multidimensional distributions. In the framework where the distributions can be modeled as i.i.d realizations of a measure on the set of distributions, we prove that the kernel defined as the quadratic distance between the...

IV regression in the context of a re-sampling is considered in the work. Comparatively, the contribution in the development is a structural identication in the IV model. The work also contains a multiplier-bootstrap justication.

Understanding the topological structure of real world networks is of huge interest in a variety of fields. One of the way to investigate this structure is to find the groups of densely connected nodes called communities. This paper presents a new non-parametric method of community detection in...

Over recent years, a study on risk management has been prompted by the Basel committee for regular banking supervisory. There are however limitations of some widely-used risk management methods that either calculate risk measures under the Gaussian distributional assumption or involve numerical...

We consider the possibility of optimal choice of observation window in the problem of parameter estimation by the observations of an inhomogeneous Poisson process. A minimax lower bound is proposed for the risk of estimation under an arbitrary choice of observation window. Then the adaptive...

Price variations at speculative markets exhibit positive autocorrelation and cross correlation. Due to large parameter spaces necessary for joint modeling of variances and covariances, multivariate parametric volatility models become easily intractable in practice. We propose an adaptive...

Risk management technology applied to high dimensional portfolios needs simple and fast methods for calculation of Value-at-Risk (VaR). The multivariate normal framework provides a simple off-the-shelf methodology but lacks the heavy tailed distributional properties that are observed in data. A...