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Martin Beckmann is going to celebrate his sixtieth birthday. This
is almost unbelievable considering the vitality, ingenuity, and
activity which he continues to show as he always did. It is an
honor able and pleasant duty for the whole economics community to
show hirn the respect, gratitude, and affection which he deserves.
Thus, those' who have contributed to this festschrift may be
thought of as a dele gation from a much larger community in which
all of us are joined; the editors in particular feel deeply
connected with and enriched by the personality and scientific work
of Martin Beckmann. Martin Beckmann is one of those rare scholars
who are not narrow minded specialists in one field; he has been
active in many areas of economics and operations research which
rapidly developed since World War 11, and he has contributed
original and fruitful ideas in almost all of them. The variety of
topics treated in this volume aims to re flect the impressive width
of his scientific interests."
The lift zonoid approach is based on a new representation of probability measures: a d-variate probability measure is represented by a convex set, its lift zonoid. First, lift zonoids are useful in data analysis to describe an empiricaldistribution by central (so-called trimmed) regions. They give rise to a concept of data depth related to the mean which is also useful in nonparametric tests for location and scale. Second, for comparing random vectors, the set inclusion of lift zonoids defines a stochastic order that reflects the dispersion of random vectors. This has many applications to stochastic comparison problems in economics and other fields. This monograph ves the first account in book form of the theory of lift zonoids and demonstrates its usefulness in multivariate analysis. Chapter 1 offers the reader an informal introduction to basic ideas, Chapter 2 presents a comprehensive investigation into the theory. The remaining seven chapters treat various applications of the lift zonoid approach and may be separately studied. Readers are assumed to have a firm grounding in probability at the graduate level. Karl Mosler is Professor of Statistics and Econometrics at the University of Cologne. He is Editor of the Allgemeines Statistisches Archive, Journal of the German Statistical Society, and has authored numerous research articles and four books (all with Springer-Verlag) in statistics and operations research.
A bibliography on stochastic orderings. Was there a real need for
it? In a time of reference databases as the MathSci or the Science
Citation Index or the Social Science Citation Index the answer
seems to be negative. The reason we think that this bibliog raphy
might be of some use stems from the frustration that we, as workers
in the field, have often experienced by finding similar results
being discovered and proved over and over in different journals of
different disciplines with different levels of mathematical so
phistication and accuracy and most of the times without cross
references. Of course it would be very unfair to blame an
economist, say, for not knowing a result in mathematical physics,
or vice versa, especially when the problems and the languages are
so far apart that it is often difficult to recognize the analogies
even after further scrutiny. We hope that collecting the references
on this topic, regardless of the area of application, will be of
some help, at least to pinpoint the problem. We use the term
stochastic ordering in a broad sense to denote any ordering
relation on a space of probability measures. Questions that can be
related to the idea of stochastic orderings are as old as
probability itself. Think for instance of the problem of comparing
two gambles in order to decide which one is more favorable."
The 17th Symposium on Operations Research was held at UniversitAt
der Bundeswehr Hamburg, August 25-28, 1992, as the annual meeting
of the Gesellschaft fA1/4r Mathematik, A-konomie und Operations
Research (GMA-OR). The aim of this book is to provide a timely and
comprehensive documentation of the symposium's scientific
activities. It contains extended abstracts of most of the papers
presented there. The symposium fell into twelve sections and an
overlapping cross-section workshop. The sections covered
established fields of theory and application such as (1)
Mathematical Modelling in OR, (2) Stochastic Models of OR, (3)
Combinatorial Optimization and Discrete Mathematics, (4) Linear and
Non-Linear Optimization, (5) Systems and Control Theory, (6)
Decision Support and Information Systems, (7) Applications in
Business and Economics, (8) Econometrics and Statistics, (9)
Micro-Economics and Game Theory, Macro-Economics and Applied
Economics, Decision Theory, Utility and Risk, Banking, Finance and
Insurance. As a novelty and an experiment, a cross-section workshop
on Environmental Systems and Economics had been included in the
program which was devoted to a topic of current political and
scientific interest.
Das Buch bietet eine Einfuhrung in die wichtigsten Methoden der
Wahrscheinlichkeitsrechnung und des statistischen Schliessens, das
heisst, der Schatzung von Parametern und des Testens von
Hypothesen. Die Autoren bemuhen sich um klare Begrifflichkeiten,
nachvollziehbare Verfahren und Motivation aus den
Wirtschaftswissenschaften. Der Band enthalt zahlreiche
durchgerechnete Beispiele sowie Hinweise zur Anwendung mit Excel
(R) und SPSS (R). Das Lehrbuch richtet sich insbesondere an
Studierende der Wirtschafts- und Sozialwissenschaften im
Grundstudium.
Das Buch bietet eine Einfuhrung in die wichtigsten Methoden der
beschreibenden Statistik und ausgewahlte Kapitel der
Wirtschaftsstatistik, insbesondere in die Indexzahlen und die
Messung von Konzentration und Disparitat. Die Darstellung zielt auf
klare Begriffe, nachvollziehbare Verfahren und Motivation aus den
Wirtschaftswissenschaften. Sie enthalt zahlreiche durchgerechnete
Beispiele, zum Teil mit aktuellen realen Wirtschaftsdaten.
Anleitungen zur Datenanalyse am Computer mit Excel(r) erganzen den
Text. Das Lehrbuch richtet sich an Studierende insbesondere der
Wirtschafts- und Sozialwissenschaften im Bachelorstudium. Es ist
auch zum Selbststudium geeignet."
Das Buch bietet eine Einfuhrung in die wichtigsten mathematischen
Methoden fur OEkonomen. Dazu gehoeren das Optimieren von Funktionen
mit und ohne Nebenbedingungen, das Loesen linearer
Gleichungssysteme, die Analyse von Differential- und
Differenzengleichungen sowie die lineare Optimierung. Die Autoren
legen besonderen Wert auf die Darstellung relevanter
wirtschaftswissenschaftlicher Begriffe und Modelle. Eine
ubersichtliche Darstellung, zahlreiche Abbildungen sowie
durchgerechnete Beispiele und Aufgaben mit Kurzloesungen
erleichtern das Selbststudium.
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