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This is the first full-length study of how the theory of random sets can be applied in econometrics.
This monograph, now in a thoroughly revised second edition, offers the latest research on random sets. It has been extended to include substantial developments achieved since 2005, some of them motivated by applications of random sets to econometrics and finance. The present volume builds on the foundations laid by Matheron and others, including the vast advances in stochastic geometry, probability theory, set-valued analysis, and statistical inference. It shows the various interdisciplinary relationships of random set theory within other parts of mathematics, and at the same time fixes terminology and notation that often vary in the literature, establishing it as a natural part of modern probability theory and providing a platform for future development. It is completely self-contained, systematic and exhaustive, with the full proofs that are necessary to gain insight. Aimed at research level, Theory of Random Sets will be an invaluable reference for probabilists; mathematicians working in convex and integral geometry, set-valued analysis, capacity and potential theory; mathematical statisticians in spatial statistics and uncertainty quantification; specialists in mathematical economics, econometrics, decision theory, and mathematical finance; and electronic and electrical engineers interested in image analysis.
This edited book contains several state-of-the-art papers devoted to econometrics of risk. Some papers provide theoretical analysis of the corresponding mathematical, statistical, computational, and economical models. Other papers describe applications of the novel risk-related econometric techniques to real-life economic situations. The book presents new methods developed just recently, in particular, methods using non-Gaussian heavy-tailed distributions, methods using non-Gaussian copulas to properly take into account dependence between different quantities, methods taking into account imprecise ("fuzzy") expert knowledge, and many other innovative techniques. This versatile volume helps practitioners to learn how to apply new techniques of econometrics of risk, and researchers to further improve the existing models and to come up with new ideas on how to best take into account economic risks.
This book overviews latest ideas and developments in financial econometrics, with an emphasis on how to best use prior knowledge (e.g., Bayesian way) and how to best use successful data processing techniques from other application areas (e.g., from quantum physics). The book also covers applications to economy-related phenomena ranging from traditionally analyzed phenomena such as manufacturing, food industry, and taxes, to newer-to-analyze phenomena such as cryptocurrencies, influencer marketing, COVID-19 pandemic, financial fraud detection, corruption, and shadow economy. This book will inspire practitioners to learn how to apply state-of-the-art Bayesian, quantum, and related techniques to economic and financial problems and inspire researchers to further improve the existing techniques and come up with new techniques for studying economic and financial phenomena. The book will also be of interest to students interested in latest ideas and results.
Handbook of Econometrics, Volume 7A, examines recent advances in foundational issues and "hot" topics within econometrics, such as inference for moment inequalities and estimation of high dimensional models. With its world-class editors and contributors, it succeeds in unifying leading studies of economic models, mathematical statistics and economic data. Our flourishing ability to address empirical problems in economics by using economic theory and statistical methods has driven the field of econometrics to unimaginable places. By designing methods of inference from data based on models of human choice behavior and social interactions, econometricians have created new subfields now sufficiently mature to require sophisticated literature summaries. - Presents a broader and more comprehensive view of this expanding field than any other handbook - Emphasizes the connection between econometrics and economics - Highlights current topics for which no good summaries exist
In economics, many quantities are related to each other. Such economic relations are often much more complex than relations in science and engineering, where some quantities are independence and the relation between others can be well approximated by linear functions. As a result of this complexity, when we apply traditional statistical techniques - developed for science and engineering - to process economic data, the inadequate treatment of dependence leads to misleading models and erroneous predictions. Some economists even blamed such inadequate treatment of dependence for the 2008 financial crisis. To make economic models more adequate, we need more accurate techniques for describing dependence. Such techniques are currently being developed. This book contains description of state-of-the-art techniques for modeling dependence and economic applications of these techniques. Most of these research developments are centered around the notion of a copula - a general way of describing dependence in probability theory and statistics. To be even more adequate, many papers go beyond traditional copula techniques and take into account, e.g., the dynamical (changing) character of the dependence in economics.
This book provides the ultimate goal of economic studies to predict how the economy develops—and what will happen if we implement different policies. To be able to do that, we need to have a good understanding of what causes what in economics. Prediction and causality in economics are the main topics of this book's chapters; they use both more traditional and more innovative techniques—including quantum ideas -- to make predictions about the world economy (international trade, exchange rates), about a country's economy (gross domestic product, stock index, inflation rate), and about individual enterprises, banks, and micro-finance institutions: their future performance (including the risk of bankruptcy), their stock prices, and their liquidity. Several papers study how COVID-19 has influenced the world economy. This book helps practitioners and researchers to learn more about prediction and causality in economics -- and to further develop this important research direction.
This is the first systematic exposition of random sets theory since Matheron (1975), with full proofs, exhaustive bibliographies and literature notes Interdisciplinary connections and applications of random sets are emphasized throughout the book An extensive bibliography in the book is available on the Web at http://liinwww.ira.uka.de/bibliography/math/random.closed.sets.html, and is accompanied by a search engine
This is the second of two volumes containing papers and commentaries presented at the Eleventh World Congress of the Econometric Society, held in Montreal, Canada in August 2015. These papers provide state-of-the-art guides to the most important recent research in economics. The book includes surveys and interpretations of key developments in economics and econometrics, and discussion of future directions for a wide variety of topics, covering both theory and application. These volumes provide a unique, accessible survey of progress on the discipline, written by leading specialists in their fields. The second volume addresses topics such as big data, macroeconomics, financial markets, and partially identified models.
R is a language and environment for data analysis and graphics. It may be considered an implementation of S, an award-winning language initially - veloped at Bell Laboratories since the late 1970s. The R project was initiated by Robert Gentleman and Ross Ihaka at the University of Auckland, New Zealand, in the early 1990s, and has been developed by an international team since mid-1997. Historically, econometricians have favored other computing environments, some of which have fallen by the wayside, and also a variety of packages with canned routines. We believe that R has great potential in econometrics, both for research and for teaching. There are at least three reasons for this: (1) R is mostly platform independent and runs on Microsoft Windows, the Mac family of operating systems, and various ?avors of Unix/Linux, and also on some more exotic platforms. (2) R is free software that can be downloaded and installed at no cost from a family of mirror sites around the globe, the Comprehensive R Archive Network (CRAN); hence students can easily install it on their own machines. (3) R is open-source software, so that the full source code is available and can be inspected to understand what it really does, learn from it, and modify and extend it. We also like to think that platform independence and the open-source philosophy make R an ideal environment for reproducible econometric research.