We propose a new statistical procedure able in some way to overcome the curse of dimensionality without structural assumptions on the function to estimate. It relies on a least-squares type penalized criterion and a new collection of models built from hyperbolic biorthogonal wavelet bases. We study its properties in a unifying intensity estimation framework, where an oracle-type inequality and ...

Except for certain parameter values, a closed form formula the mode of generalized hyperbolic (GH) distribution is not available. In this paper, we exploit results from literature on modified Bessel functions and their ratios to obtain simple but tight two-sided inequalities GH general values. As special case, deduce variance-gamma (VG) distribution, through similar approach also McKay Type I d...

This paper introduces a novel methodology to perform topological regularization in multivariate probabilistic modeling by using sparse, complex, networks which represent the system’s dependency structure and are called information filtering (IFN). can be directly applied covariance selection problem providing an instrument for sparse with both linear non-linear probability distributions such as...

We give a rigorous geometric proof of the Murakami-Yano formula for the volume of a hyperbolic tetrahedron. In doing so, we are led to consider generalized hyperbolic tetrahedra, which are allowed to be non-convex, and have vertices ‘beyond infinity’; and we uncover a group, which we call 22.5K, of 23040 = 30 · 12 · 2 scissors-class-preserving symmetries of the space of (suitably decorated) gen...

In this paper, we consider the multivariate Bernoulli distribution as a model to estimate the structure of graphs with binary nodes. This distribution is discussed in the framework of the exponential family, and its statistical properties regarding independence of the nodes are demonstrated. Importantly the model can estimate not only the main effects and pairwise interactions among the nodes b...

Abstract: The Multivariate Extreme Value distributions have shown their usefulness in environmental studies, financial and insurance mathematics. The Logistic or Gumbel-Hougaard distribution is one of the oldest multivariate extreme value models and it has been extended to asymmetric models. In this paper we introduce generalized logistic multivariate distributions. Our tools are mixtures of co...

The Multivariate Extreme Value distributions have shown their usefulness in environmental studies, financial and insurance mathematics. The Logistic or Gumbel–Hougaard distribution is one of the oldest multivariate extreme value models and it has been extended to asymmetric models. In this paper we introduce generalized logistic multivariate distributions. Our tools are mixtures of copulas and ...