In this paper we introduce generalized S-estimators for the multivariate regression model. This class of estimators combines high robustness and high efficiency. They are defined by minimizing the determinant of a robust estimator of the scatter matrix of differences of residuals. In the special case of a multivariate location model, the generalized S-estimator has the important independence pr...

We study the multivariate approximation by certain partial sums (hyperbolic wavelet sums) of wavelet bases formed by tensor products of univariate wavelets. We characterize spaces of functions which have a prescribed approximation error by hyperbolic wavelet sums in terms of a K -functional and interpolation spaces. The results parallel those for hyperbolic trigonometric cross approximation of ...

For relatively hyperbolic groups, we investigate conditions under which the subgroup generated by two quasiconvex subgroups Q1 and Q2 is quasiconvex and isomorphic to Q1 ∗Q1∩Q2 Q2. Our results generalized known combination theorems for quasiconvex subgroups of word-hyperbolic groups. Some applications are presented. In addition, it is proved that the intersection of quasiconvex subgroups is qua...

We propose a new model for dynamic volatilities and correlations of skewed and heavytailed data. Our model endows the Generalized Hyperbolic distribution with time-varying parameters driven by the score of the observation density function. The key novelty in our approach is the fact that the skewed and fat-tailed shape of the distribution directly affects the dynamic behavior of the time-varyin...

This article provides an introduction to the normative approach to inequality measurement. Multivariate generalizations of the procedures used to construct univariate inequality indices from social evaluation orderings are described. Axiomatizations of multivariate Atkinson, Kolm– Pollak, and generalized Gini indices are discussed. Maasoumi’s [Econometrica (1986)] two-stage procedure for constr...

In this paper, we considered the half logistic model and derived a probability density function that generalized it. The cumulative distribution function, the $n^{th}$ moment, the median, the mode and the 100$k$-percentage points of the generalized distribution were established. Estimation of the parameters of the distribution through maximum likelihood method was accomplished with the aid of c...

A Kac-Moody algebra is called hyperbolic if it corresponds to a generalized Cartan matrix of hyperbolic type. We study root subsystems of root systems of hyperbolic algebras. In this paper, we classify maximal rank regular hyperbolic subalgebras of hyperbolic Kac-Moody algebras. Introduction A generalized Cartan matrix A is called a matrix of hyperbolic type if it is indecomposable symmetrizabl...

When forecasts are assessed by a general loss (cost-of-error) function, the optimal point forecast is not, in general, the conditional mean, and depends on the conditional volatility – which, for stock returns, is time-varying. Our aim is to provide forecasts of daily returns of 30 DJIA stocks under a general multivariate loss function. The paper’s contributions are as follows. We discuss what ...