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Goodness Of Fit Statistics For Discrete Multivariate Data

Author: Timothy R.C. Read
Publisher: Springer Science & Business Media
ISBN: 1461245788
Size: 65.59 MB
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The statistical analysis of discrete multivariate data has received a great deal of attention in the statistics literature over the past two decades. The develop ment ofappropriate models is the common theme of books such as Cox (1970), Haberman (1974, 1978, 1979), Bishop et al. (1975), Gokhale and Kullback (1978), Upton (1978), Fienberg (1980), Plackett (1981), Agresti (1984), Goodman (1984), and Freeman (1987). The objective of our book differs from those listed above. Rather than concentrating on model building, our intention is to describe and assess the goodness-of-fit statistics used in the model verification part of the inference process. Those books that emphasize model development tend to assume that the model can be tested with one of the traditional goodness-of-fit tests 2 2 (e.g., Pearson's X or the loglikelihood ratio G ) using a chi-squared critical value. However, it is well known that this can give a poor approximation in many circumstances. This book provides the reader with a unified analysis of the traditional goodness-of-fit tests, describing their behavior and relative merits as well as introducing some new test statistics. The power-divergence family of statistics (Cressie and Read, 1984) is used to link the traditional test statistics through a single real-valued parameter, and provides a way to consolidate and extend the current fragmented literature. As a by-product of our analysis, a new 2 2 statistic emerges "between" Pearson's X and the loglikelihood ratio G that has some valuable properties.

Handbook Of Computational Statistics

Author: James E. Gentle
Publisher: Springer Science & Business Media
ISBN: 3642215513
Size: 72.30 MB
Format: PDF, Docs
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The Handbook of Computational Statistics - Concepts and Methods (second edition) is a revision of the first edition published in 2004, and contains additional comments and updated information on the existing chapters, as well as three new chapters addressing recent work in the field of computational statistics. This new edition is divided into 4 parts in the same way as the first edition. It begins with "How Computational Statistics became the backbone of modern data science" (Ch.1): an overview of the field of Computational Statistics, how it emerged as a separate discipline, and how its own development mirrored that of hardware and software, including a discussion of current active research. The second part (Chs. 2 - 15) presents several topics in the supporting field of statistical computing. Emphasis is placed on the need for fast and accurate numerical algorithms, and some of the basic methodologies for transformation, database handling, high-dimensional data and graphics treatment are discussed. The third part (Chs. 16 - 33) focuses on statistical methodology. Special attention is given to smoothing, iterative procedures, simulation and visualization of multivariate data. Lastly, a set of selected applications (Chs. 34 - 38) like Bioinformatics, Medical Imaging, Finance, Econometrics and Network Intrusion Detection highlight the usefulness of computational statistics in real-world applications.

Multivariate Statistical Modelling Based On Generalized Linear Models

Author: Ludwig Fahrmeir
Publisher: Springer Science & Business Media
ISBN: 1489900101
Size: 28.65 MB
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Concerned with the use of generalised linear models for univariate and multivariate regression analysis, this is a detailed introductory survey of the subject, based on the analysis of real data drawn from a variety of subjects such as the biological sciences, economics, and the social sciences. Where possible, technical details and proofs are deferred to an appendix in order to provide an accessible account for non-experts. Topics covered include: models for multi-categorical responses, model checking, time series and longitudinal data, random effects models, and state-space models. Throughout, the authors have taken great pains to discuss the underlying theoretical ideas in ways that relate well to the data at hand. As a result, numerous researchers whose work relies on the use of these models will find this an invaluable account.

Asymptotic Theory Of Statistical Inference For Time Series

Author: Masanobu Taniguchi
Publisher: Springer Science & Business Media
ISBN: 146121162X
Size: 60.68 MB
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The primary aim of this book is to provide modern statistical techniques and theory for stochastic processes. The stochastic processes mentioned here are not restricted to the usual AR, MA, and ARMA processes. A wide variety of stochastic processes, including non-Gaussian linear processes, long-memory processes, nonlinear processes, non-ergodic processes and diffusion processes are described. The authors discuss estimation and testing theory and many other relevant statistical methods and techniques.

Geometrical Foundations Of Asymptotic Inference

Author: Robert E. Kass
Publisher: Wiley-Interscience
Size: 51.50 MB
Format: PDF
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Differential geometry provides an aesthetically appealing and often revealing view of statistical inference. Beginning with an elementary treatment of one-parameter statistical models and ending with an overview of recent developments, this is the first book to provide an introduction to the subject that is largely accessible to readers not already familiar with differential geometry. It also gives a streamlined entry into the field to readers with richer mathematical backgrounds. Much space is devoted to curved exponential families, which are of interest not only because they may be studied geometrically but also because they are analytically convenient, so that results may be derived rigorously. In addition, several appendices provide useful mathematical material on basic concepts in differential geometry. Topics covered include the following: * Basic properties of curved exponential families * Elements of second-order, asymptotic theory * The Fisher-Efron-Amari theory of information loss and recovery * Jeffreys-Rao information-metric Riemannian geometry * Curvature measures of nonlinearity * Geometrically motivated diagnostics for exponential family regression * Geometrical theory of divergence functions * A classification of and introduction to additional work in the field

The Multivariate Normal Distribution

Author: Yung Liang Tong
Publisher: Springer Verlag
ISBN: 9780387970622
Size: 36.41 MB
Format: PDF
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This book represents a comprehensive and coherent treatment of the results related to the multivariate normal distribution. In addition to the classical topics on distribution theory, correlation analysis and sampling distributions, it also contains important results reported recently in the literature, but which cannot be found in most books on multivariate analysis. The material is organized in a unified modern approach, and the main themes are dependence, probability inequalities, and their roles in theory and applications. Some of the properties (such as log-concavity, unimodality, Schurconcavity and total positivity) of a multivariate normal density function are discussed, and results that follow from these properties and reviewed extensively. The volume also includes tables of the equi-coordinate percentage points and probability inequalities for exchangeable normal variables. The volume is accessible to graduate students and advanced undergraduates in statistics, mathematics, and related applied areas, and can be used as a reference in a course on multivariate analysis.

Test Equating

Author: Michael J. Kolen
Publisher: Copernicus
ISBN: 9780387944869
Size: 45.14 MB
Format: PDF, ePub
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Many researchers in the psychology and statistical communities have paid increasing attention to test equating as issues of using multiple test forms have arisen and in response to criticisms of traditional testing techniques. This text provides a practically-oriented introduction to test equating, covering discussions of the most frequently used equating methodologies and many of the practical issues involved. The main themes covered bu the book are: the purposes and assumptions of equating; classical equating methods; item response theory equating methods; standard errors of equating; and practical issues in equating.