2007, XII, 456 p., Softcover
ISBN: 978-3-540-72243-4
About this textbook
Wide scope of methods and applications
Quantlets in R and Matlab available online
Many examples and exercises
Most of the observable phenomena in the empirical sciences are of a multivariate nature.In financial studies, assets in stock markets are observed simultaneously and their joint development is analyzed to better understand general tendencies and to track indices. In medicine recorded observations of subjects in different locations are the basis of reliable diagnoses and medication. In quantitative marketing consumer preferences are collected in order to construct models of consumer behavior. The underlying theoretical structure of these and many other quantitative studies of applied sciences is multivariate. Focussing on applications this book presents the tools and concepts of multivariate data analysis in a way that is understandable for non-mathematicians and practitioners who face statistical data analysis.
In this second edition a wider scope of methods and applications of multivariate statistical analysis is introduced. All quantlets have been translated into the R and Matlab language and are made available online.
Table of contents
I Descriptive Techniques: Comparison of Batches.- II Multivariate Random Variables: A Short Excursion into Matrix Algebra; Moving to Higher Dimensions; Multivariate Distributions; Theory of the Multinormal; Theory of Estimation; Hypothesis Testing.- III Multivariate Techniques: Decomposition of Data Matrices by Factors; Principal Components Analysis; Factor Analysis; Cluster Analysis; Discriminant Analysis.- Correspondence Analysis.- Canonical Correlation Analysis.- Multidimensional Scaling.- Conjoint Measurement Analysis.- Application in Finance.- Computationally Intensive Techniques.- A: Symbols and Notations.- B: Data.- Bibliography.- Index.
2007, X, 274 p., 43 illus., Hardcover
ISBN: 978-3-540-73290-7
About this book
This book presents modern developments in time series econometrics that are applied to macroeconomic and financial time series. It bridges the gap between methods and realistic applications. This book contains the most important approaches to analyze time series which may be stationary or nonstationary. It starts with modeling and forecasting univariate time series and then presents Granger causality tests and vector autoregressive models for multiple stationary time series.
For real applied work the modeling of nonstationary uni- or multivariate time series is most important. Therefore, unit root and cointegration analysis as well as vector error correction models play a central part. Modelling volatilities of financial time series with autoregressive conditional heteroskedastic models is also treated.
Written for:
Students, researchers
Keywords:
Cointegration
Granger Causality
Unit Roots
Vector Autoregressive Models
Volatility
Table of contents
Introduction and Basics.- Univariate Stationary Processes.- Granger Causality.- Vector Autoregressive Processes.- Nonstationary Processes.- Cointegration.- Autoregressive Conditional Heteroskedasticity
Series: Trends in Logic , Vol. 25
2007, Approx. 220 p., 5 illus., Hardcover
ISBN: 978-1-4020-6163-9
About this book
Goguen categories extend the relational calculus and its categorical formalization to the fuzzy world. Starting from the fundamental concepts of sets, binary relations and lattices this book introduces several categorical formulations of an abstract theory of relations such as allegories, Dedekind categories and related structures. It is shown that neither theory is sufficiently rich to describe basic operations on fuzzy relations. The book then introduces Goguen categories and provides a comprehensive study of these structures including their representation theory, and the definability of norm-based operations.
The power of the theory is demonstrated by a comprehensive example. A certain Goguen category is used to specify and to develop a fuzzy controller. Based on its abstract description as well as certain desirable properties and their formal proofs, a verified controller is derived without compromising the - sometimes - intuitive choice of norm-based operations by fuzzy engineers.
Written for:
Mathematicians/computer scientists working in fuzzy logic, researchers in formal logics and the relation algebras
Keywords:
Allegories
Categories
Computer science
Fuzzy relations
Goguen
Relation algebras
Table of contents
Preface.- Introduction.- 1. Sets, Relations, and Functions.- 2. Lattices.- 3. L-fuzzy Relations.- 4. Categories of Relations.- 5. Categories of L-fuzzy Relations.- 6. Fuzzy Controllers in Goguen Categories.- Index.- Symbols.- References.
2007, XXII, 486 p., 212 illus., Hardcover
ISBN: 978-0-387-73057-8
About this textbook
Excellent coverage of topics such as series, residues and the evaluation of integrals, multi-valued functions, conformal mapping, dispersion relations and analytic continuation
Systematic and clear presentation with many diagrams to clarify discussion of the material
Numerous worked examples and a large number of assigned problems
Complex Analysis with Applications in Science and Engineering weaves together theory and extensive applications in mathematics, physics and engineering. In this edition there are many new problems, revised sections, and an entirely new chapter on analytic continuation. This work will serve as a textbook for undergraduate and graduate students in the areas noted above.
Key Features of this Second Edition:
Excellent coverage of topics such as series, residues and the evaluation of integrals, multivalued functions, conformal mapping, dispersion relations and analytic continuation
Systematic and clear presentation with many diagrams to clarify discussion of the material
Numerous worked examples and a large number of assigned problems
Table of contents
Introduction.- Complex Numbers.- Complex Variables.- Series, Limits and Residues.- Evaluation of Integrals.- Multivalued Functions, Branch Points and Cuts.- Singularities of Functions Defined by Integrals.- Conformal Mapping.- Dispersion Relations.- Analytic Continuation.- Appendix 1.- Appendix 2.- Appendix 3.- Appendix 4.- Appendix 5.- Appendix 6.- Appendix 7.- Appendix 8.- References.- Index.
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Series: Springer Texts in Statistics
2008, XVI, 472 p., Hardcover
ISBN: 978-0-387-98735-4
About this textbook
Text for competent practitioners of statistics, not future statisticians
Suitable as reference
Studying Human Populations is a textbook for graduate students and research workers in social statistics and related subject areas. It follows a novel curriculum developed around the basic statistical activities: sampling, measurement and inference. Statistics is defined broadly as making decisions in the presence of uncertainty that arise as a consequence of limited resources available for collecting information. A connecting link of the presented methods is the perspective of missing information, catering for a diverse class of problems that include nonresponse, imperfect measurement and causal inference. In principle, any problem too complex for our limited analytical toolkit could be converted to a tractable problem if some additional information were available. Ingenuity is called for in declaring such (missing) information constructively, but the universe of problems that we can address is wide open, not limited by a discrete set of procedures.
The monograph aims to prepare the reader for the career of an independent social statistician and to serve as a reference for methods, ideas for and ways of studying of human populations: formulation of the inferential goals, design of studies, search for the sources of relevant information, analysis and presentation of results. Elementary linear algebra and calculus are prerequisites, although the exposition is quite forgiving, especially in the first few lectures. Familiarity with statistical software at the outset is an advantage, but it can be developed while reading the first few chapters.
Nicholas T. Longford directs the statistical research and consulting company SNTL in Reading, England. He had held senior research posts at the Educational Testing Service, Princeton, NJ, and De Montfort University, Leicester, England. He was awarded the first Campion Fellowship by the Royal Statistical Society (2000-2002). He is a member of the editorial boards of the British Journal of Mathematical and Statistical Psychology and of Survey Research Methods, and a former Associate Editor of the Journal of Educational and Behavioral Statistics, Journal of Multivariate Analysis and Journal of the Royal Statistical Society Series A and D. He is the author of three other monographs, the latest entitled Missing Data and Small-Area Estimation (Springer, 2005).
Table of contents
Anova and Ordinary Regression.- Maximum Likelihood Estimation.- Sampling Methods.- The Bayesian Paradigm.- Incomplete Data.- Imperfect Measurement.- Experiments and Observational Studies.- Clinical Trials.- Random Coefficients.- Generalised Linear Models.- Longitudinal and Time-Series Analysis.- Meta-Analysis and Estimating Many Quantities.
Series: Sources and Studies in the History of Mathematics and Physical Sciences
2008, Approx. 375 p., 21 illus., Hardcover
ISBN: 978-0-387-73467-5
About this book
Carefully researched, accompanied by detailed bibliography
Provides a coherent and detailed account of the theory of series in the 18th and early 19th centuries
Includes a comprehensive account of many results that were previously scattered throughout the historical and textbook literature
The manuscript gives a coherent and detailed account of the theory of series in the eighteenth and early nineteenth centuries. It provides in one place an account of many results that are generally to be found - if at all - scattered throughout the historical and textbook literature. It presents the subject from the viewpoint of the mathematicians of the period, and is careful to distinguish earlier conceptions from ones that prevail today.
Table of contents
Preface.- Part I: From the beginnings of the seventeenth century to about 1720: convergence and formal manipulation.- Series before the rise of the calculus.- Geometrical quantities and series in Leibniz.- The Bernoulli series and Leibniz's analogy.- Newton's method of series.- Jacob Bernoulli's treatise on series.- The Taylor series.- Quantities and their representations.- The formal-quantitative theory of series.- The first appearance of divergent series.- Part II: From 1720s to 1760s: The development of a more formal conception.- De Moivre's recurrent seires and Bernoulli's method.- Acceleration of series and Stirling's series.- Maclaurin's contribution.- The young Euler between innovation and tradition.- Euler's derivation of the Euler-Maclaurin summation formula.- On the sum of an asymptotic series.- Infinite products and continued fractions.- Series and number theory.- Anaysis after the 1740s.- The formal concept of series.- Part III: The theory of series after 1760: Successes and problems of the triumphant formalism.- Lagrange inversion theorem.- Towards the calculus of operations.- Laplace's calculus of generating functions.- The problem of analytical representation of nonelementary quantities.- Inexplicable functions.- Integration and functions.- Series and differential equations.- Trigonometric series.- Further developments of the formal theory of series.- Attemps to introduce new transcendental functions.- D'Alembert and Lagrange and the inequality technique.- Part IV: The decline of formal theory of series.- Fourier and Fourier series.- Gauss and the hypergeometric series.- Cauchy's rejections of the eighteenth-century theory of series