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...

Given data y and k covariates xj one problem in linear regression is to decide which if any of the covariates to include when regressing the dependent variable y on the covariates xj . In this paper three such methods, lasso, knockoff and Gaussian covariates are compared using simulations and...

In this paper, we propose a new class of regime shift models with exible switching mechanism that relies on a nonparametric probability function of the observed thresh- old variables. The proposed models generally embrace traditional threshold models with contaminated threshold variables or...

Let X1, . . . ,Xn be i.i.d. sample in Rp with zero mean and the covariance matrix . The problem of recovering the projector onto an eigenspace of from these observations naturally arises in many applications. Recent technique from [9] helps to study the asymp- totic distribution of the distance...

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...