This paper presents a new approach to non-parametric cluster analysis called Adaptive Weights Clustering (AWC). The idea is to identify the clustering structure by checking at different points and for dierent scales on departure from local homogeneity. The proposed procedure describes the...

In this paper, we consider a probabilistic setting where the probability measures are considered to be random objects. We propose a procedure of construction non-asymptotic confidence sets for empirical barycenters in 2 -Wasserstein space and develop the idea further to construction of a...

We derive tight non-asymptotic bounds for the Kolmogorov distance between the probabilities of two Gaussian elements to hit a ball in a Hilbert space. The key property of these bounds is that they are dimension-free and depend on the nuclear (Schatten-one) norm of the difference between the...

Let X1; : : : ;Xn be i.i.d. sample in Rp with zero mean and the covariance matrix . The classic principal component analysis esti- mates the projector P J onto the direct sum of some eigenspaces of by its empirical counterpart bPJ . Recent papers [20, 23] investigate the asymptotic distribution...

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.

We investigate correlations of asset returns in stress scenarios where a common risk factor is truncated. Our analysis is performed in the class of normal variance mixture (NVM) models, which encompasses many distributions commonly used in nancial modelling. For the special cases of jointly...

We investigate default probabilities and default correlations of Merton-type credit portfolio models in stress scenarios where a common risk factor is truncated. The analysis is performed in the class of elliptical distributions, a family of light-tailed to heavy-tailed distributions...