High dimensional predictive regressions are useful in wide range of applications. However, the theory is mainly developed assuming that model stationary with time invariant parameters. This at odds prevalent evidence for parameter instability economic series, but theories models a small number covariates. In this paper, we present two L2 boosting algorithms estimating high which coefficients mo...

A positively convex module is a non-empty set closed under positively convex combinations but not necessarily a subset of a linear space. Positively convex modules are a natural generalization of positively convex subsets of linear spaces. Any positively convex module has a canonical semimetric and there is a universal positively affine mapping into a regularly ordered normed linear space and a...

In this talk, we discuss the maximum number of n × n pure imaginary quaternionic solutions to the Hurwitz matrix equations given by T i T * j + T j T Abstract Let T be a bounded linear operator on a complex Hilbert space H. For 0 ≤ q ≤ 1, the

We present a novel ultimate bound and invariant set computation method for continuous-time switched linear systems with disturbances and arbitrary switching. The proposed method relies on the existence of a transformation that takes all matrices of the switched linear system into a convenient form satisfying certain properties. The method provides ultimate bounds and invariant sets in the form ...

In this paper, we propose a new componentwise estimator of a dispersion matrix, based on a highly robust estimator of scale. The key idea is the elimination of a location estimator in the dispersion estimation procedure. The robustness properties are studied by means of the influence function and the breakdown point. Further characteristics such as asymptotic variance and efficiency are also an...

The new approach of distributed graphs and graph transformation as developed in this article allows to use structured graph transformation on two abstraction levels, the network and the local level. The network level contains the description of the topological structures of a system. The local level covers the description of states and their transitions in local systems. Local state transitions...

A Kleene algebra (K,+, ·,∗ , 0, 1) is an idempotent semiring with an iteration ∗ as axiomatised by Kozen. We consider left semiring modules (A,+, 0, :) over Kleene algebras. We call such a left semiring module a Kleene module if each linear equation x = a + r : x has a least solution, where : is the product from K × A to A. The linear context-free languages can be viewed as a Kleene module A ov...

We describe Koszul type complexes associated with a linear map from any module to a free module, and vice versa with a linear map from a free module to an arbitrary module, generalizing the classical Koszul complexes. Given a short complex of finite free modules, we assemble these complexes to what we call Koszul bicomplexes. They are used in order to investigate the homology of the Koszul comp...

Let R be a commutative ring. For two (left) R-modules M and N , the set HomR(M,N) of allR-linear maps fromM toN is anR-module under natural addition and scaling operations on linear maps. (If R were non-commutative then the definition (r · f)(m) = r · (f(m)) would yield a function r · f from M to N which is usually not R-linear. Try it!) In the special case where N = R we get the R-module M∨ = ...

In this paper, we generalize the notion of border bases of zerodimensional polynomial ideals to the module setting. To this end, we introduce order modules as a generalization of order ideals and module border bases of submodules with finite codimension in a free module as a generalization of border bases of zero-dimensional ideals in the first part of this paper. In particular, we extend the d...