Measuring the degree of association between random variables is a task inherent in many practical applications such as risk management and financial modeling. Well-known measures like Spearman's rho and Kendall's tau can be expressed in terms of the underlying copula only, hence, being independent of the underlying univariate marginal distributions. Opposed to these classical measures of association, mutual information, which is derived from information theory, constitutes a fundamentally different approach of measuring association. Although this measure is likewise independent of the univariate margins, it is not a functional of the copula but of the corresponding copula density. Besides the theoretical properties of mutual information as a measure of multivariate association, possibilities to estimate the copula density based on observations of continuous distributions are investigated. To cope with the effect of boundary bias, new estimators are introduced and existing functionals are generalized to the multivariate case. The performance of these estimators is evaluated in comparison to common kernel density estimation schemes. To facilitate variance estimation by means of resampling methods like bootstrapping, an algorithm is introduced, which significantly reduces computation time in comparison with pre-implemented algorithms. In practical applications, complete continuous data is oftentimes not available to the analyst. Instead, categorial data derived from the underlying continuous distribution may be given. Hence, estimation of the copula and its density based on contingency tables is investigated. The newly developed estimators are employed to derive estimates of Spearman's rho and Kendall's tau and their performance is compared.

Copulas are mathematical objects that fully capture the dependence structure among random variables and hence offer great flexibility in building multivariate stochastic models. Since their introduction in the early 50's, copulas have gained considerable popularity in several fields of applied mathematics, such as finance, insurance and reliability theory. Today, they represent a well-recognized tool for market and credit models, aggregation of risks, portfolio selection, etc. This book is divided into two main parts: Part I - "Surveys" contains 11 chapters that provide an up-to-date account of essential aspects of copula models. Part II - "Contributions" collects the extended versions of 6 talks selected from papers presented at the workshop in Warsaw.

This book introduces the main theoretical findings related to copulas and shows how statistical modeling of multivariate continuous distributions using copulas can be carried out in the R statistical environment with the package copula (among others). Copulas are multivariate distribution functions with standard uniform univariate margins. They are increasingly applied to modeling dependence among random variables in fields such as risk management, actuarial science, insurance, finance, engineering, hydrology, climatology, and meteorology, to name a few. In the spirit of the Use R! series, each chapter combines key theoretical definitions or results with illustrations in R. Aimed at statisticians, actuaries, risk managers, engineers and environmental scientists wanting to learn about the theory and practice of copula modeling using R without an overwhelming amount of mathematics, the book can also be used for teaching a course on copula modeling.

Copulas are functions that join multivariate distribution functions to their one-dimensional margins. The study of copulas and their role in statistics is a new but vigorously growing field. In this book the student or practitioner of statistics and probability will find discussions of the fundamental properties of copulas and some of their primary applications. The applications include the study of dependence and measures of association, and the construction of families of bivariate distributions. With nearly a hundred examples and over 150 exercises, this book is suitable as a text or for self-study. The only prerequisite is an upper level undergraduate course in probability and mathematical statistics, although some familiarity with nonparametric statistics would be useful. Knowledge of measure-theoretic probability is not required. Roger B. Nelsen is Professor of Mathematics at Lewis & Clark College in Portland, Oregon. He is also the author of "Proofs Without Words: Exercises in Visual Thinking," published by the Mathematical Association of America.

Contains a selection of papers presented initially at the 7th Annual Advances in Econometrics Conference held on the LSU campus in Baton Rouge, Louisiana during November 14-16, 2008. This work is suitable for those who wish to familiarize themselves with nonparametric methodology.

Handbook of Empirical Economics and Finance explores the latest developments in the analysis and modeling of economic and financial data. Well-recognized econometric experts discuss the rapidly growing research in economics and finance and offer insight on the future direction of these fields. Focusing on micro models, the first group of chapters describes the statistical issues involved in the analysis of econometric models with cross-sectional data often arising in microeconomics. The book then illustrates time series models that are extensively used in empirical macroeconomics and finance. The last set of chapters explores the types of panel data and spatial models that are becoming increasingly significant in analyzing complex economic behavior and policy evaluations. This handbook brings together both background material and new methodological and applied results that are extremely important to the current and future frontiers in empirical economics and finance. It emphasizes inferential issues that transpire in the analysis of cross-sectional, time series, and panel data-based empirical models in economics, finance, and related disciplines.

This textbook provides a step-by-step introduction to the class of vine copulas, their statistical inference and applications. It focuses on statistical estimation and selection methods for vine copulas in data applications. These flexible copula models can successfully accommodate any form of tail dependence and are vital to many applications in finance, insurance, hydrology, marketing, engineering, chemistry, aviation, climatology and health. The book explains the pair-copula construction principles underlying these statistical models and discusses how to perform model selection and inference. It also derives simulation algorithms and presents real-world examples to illustrate the methodological concepts. The book includes numerous exercises that facilitate and deepen readers’ understanding, and demonstrates how the R package VineCopula can be used to explore and build statistical dependence models from scratch. In closing, the book provides insights into recent developments and open research questions in vine copula based modeling. The book is intended for students as well as statisticians, data analysts and any other quantitatively oriented researchers who are new to the field of vine copulas. Accordingly, it provides the necessary background in multivariate statistics and copula theory for exploratory data tools, so that readers only need a basic grasp of statistics and probability.

This book gives readers the solid and formal mathematical background to apply copulas to a range of mathematical areas, such as probability, real analysis, measure theory, and algebraic structures. The authors prove the results as simply as possible and unify various methods scattered throughout the literature in common frameworks, including shuffles of copulas. They also explore connections with related functions, such as quasi-copulas, semi-copulas, and triangular norms, that have been used in different domains.

The chapters in this volume stress the need for advances in theoretical understanding to go hand-in-hand with the widespread practical application of forecasting in industry. Forecasting and time series prediction have enjoyed considerable attention over the last few decades, fostered by impressive advances in observational capabilities and measurement procedures. On June 5-7, 2013, an international Workshop on Industry Practices for Forecasting was held in Paris, France, organized and supported by the OSIRIS Department of Electricité de France Research and Development Division. In keeping with tradition, both theoretical statistical results and practical contributions on this active field of statistical research and on forecasting issues in a rapidly evolving industrial environment are presented. The volume reflects the broad spectrum of the conference, including 16 articles contributed by specialists in various areas. The material compiled is broad in scope and ranges from new findings on forecasting in industry and in time series, on nonparametric and functional methods and on on-line machine learning for forecasting, to the latest developments in tools for high dimension and complex data analysis.