633 research outputs found
Regularized Covariance Matrix Estimation in Complex Elliptically Symmetric Distributions Using the Expected Likelihood Approach - Part 1: The Over-Sampled Case
In \cite{Abramovich04}, it was demonstrated that the likelihood ratio (LR) for multivariate complex Gaussian distribution has the invariance property that can be exploited in many applications. Specifically, the probability density function (p.d.f.) of this LR for the (unknown) actual covariance matrix does not depend on this matrix and is fully specified by the matrix dimension and the number of independent training samples . Since this p.d.f. could therefore be pre-calculated for any a priori known , one gets a possibility to compare the LR of any derived covariance matrix estimate against this p.d.f., and eventually get an estimate that is statistically ``as likely'' as the a priori unknown actual covariance matrix. This ``expected likelihood'' (EL) quality assessment allows for significant improvement of MUSIC DOA estimation performance in the so-called ``threshold area'' \cite{Abramovich04,Abramovich07d}, and for diagonal loading and TVAR model order selection in adaptive detectors \cite{Abramovich07,Abramovich07b}. Recently, a broad class of the so-called complex elliptically symmetric (CES) distributions has been introduced for description of highly in-homogeneous clutter returns. The aim of this series of two papers is to extend the EL approach to this class of CES distributions as well as to a particularly important derivative of CES, namely the complex angular central distribution (ACG). For both cases, we demonstrate a similar invariance property for the LR associated with the true scatter matrix \mSigma_{0}. Furthermore, we derive fixed point regularized covariance matrix estimates using the generalized expected likelihood methodology. This first part is devoted to the conventional scenario () while Part 2 deals with the under-sampled scenario ()
Quantum control of molecular rotation
The angular momentum of molecules, or, equivalently, their rotation in
three-dimensional space, is ideally suited for quantum control. Molecular
angular momentum is naturally quantized, time evolution is governed by a
well-known Hamiltonian with only a few accurately known parameters, and
transitions between rotational levels can be driven by external fields from
various parts of the electromagnetic spectrum. Control over the rotational
motion can be exerted in one-, two- and many-body scenarios, thereby allowing
to probe Anderson localization, target stereoselectivity of bimolecular
reactions, or encode quantum information, to name just a few examples. The
corresponding approaches to quantum control are pursued within separate, and
typically disjoint, subfields of physics, including ultrafast science, cold
collisions, ultracold gases, quantum information science, and condensed matter
physics. It is the purpose of this review to present the various control
phenomena, which all rely on the same underlying physics, within a unified
framework. To this end, we recall the Hamiltonian for free rotations, assuming
the rigid rotor approximation to be valid, and summarize the different ways for
a rotor to interact with external electromagnetic fields. These interactions
can be exploited for control --- from achieving alignment, orientation, or
laser cooling in a one-body framework, steering bimolecular collisions, or
realizing a quantum computer or quantum simulator in the many-body setting.Comment: 52 pages, 11 figures, 607 reference
FEMDA: a unified framework for discriminant analysis
Although linear and quadratic discriminant analysis are widely recognized
classical methods, they can encounter significant challenges when dealing with
non-Gaussian distributions or contaminated datasets. This is primarily due to
their reliance on the Gaussian assumption, which lacks robustness. We first
explain and review the classical methods to address this limitation and then
present a novel approach that overcomes these issues. In this new approach, the
model considered is an arbitrary Elliptically Symmetrical (ES) distribution per
cluster with its own arbitrary scale parameter. This flexible model allows for
potentially diverse and independent samples that may not follow identical
distributions. By deriving a new decision rule, we demonstrate that
maximum-likelihood parameter estimation and classification are simple,
efficient, and robust compared to state-of-the-art methods
Essays on Energy Portfolio Management
Diese englischsprachige Dissertation behandelt ausgewählte Fragen zum Thema Portfoliomanagement in Energiemärkten. Im Kontext der modernen Portfoliotheorie werden theoretische Verteilungsannahmen untersucht, die einen optimalen Mittelwert-Varianz-Ansatz implizieren. Der Bereich zu Energiemärkten befasst sich einerseits mit Kurzfristprognosen von Day-Ahead-Preisen auf dem Strommarkt. Andererseits werden auf dem Erdgasmarkt die von komplexen Energiederivaten impliziten Volatilitäten analysiert. Einige interessante Beiträge, die diese Dissertation liefert, sind beispielsweise (i) die Erkenntnis, dass sich der Mittelwert-Varianz-Ansatz zur Bestimmung eines optimalen Portfolios von Vermögensgegenständen auch im Falle einer schiefen Renditeverteilung theoretisch rechtfertigen lässt, (ii) eine umfangreiche Vergleichsstudie mit verschiedenen Ansätzen zur Reduktion der Komplexität von multivariaten Strompreisprognosen und (iii) die Entwicklung eines theoretischen Rahmens und effizienten Algorithmus zur Übersetzung von Preisen für Swing-Optionen in implizite Volatilitäten
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