The Theory of Canonical Moments with Applications in Statistics Probability and Analysis

Author: Holger Dette
Publisher: John Wiley & Sons
ISBN: 0471109916
Release Date: 1997-09-08
Genre: Mathematics

This new material is concerned with the theory and applications of probability, statistics and analysis of canonical moments. It provides a powerful tool for the determination of optimal experimental designs, for the calculation of the main characteristics of random walks, and for other moment problems appearing in probability and statistics.

Methods for Statistical Data Analysis of Multivariate Observations

Author: R. Gnanadesikan
Publisher: John Wiley & Sons
ISBN: 0471161195
Release Date: 1997-02-04
Genre: Mathematics

A practical guide for multivariate statistical techniques—now updated and revised In recent years, innovations in computer technology andstatistical methodologies have dramatically altered the landscapeof multivariate data analysis. This new edition of Methods forStatistical Data Analysis of Multivariate Observations explorescurrent multivariate concepts and techniques while retaining thesame practical focus of its predecessor. It integrates methods anddata-based interpretations relevant to multivariate analysis in away that addresses real-world problems arising in many areas ofinterest. Greatly revised and updated, this Second Edition provideshelpful examples, graphical orientation, numerous illustrations,and an appendix detailing statistical software, including the S (orSplus) and SAS systems. It also offers An expanded chapter on cluster analysis that covers advances inpattern recognition New sections on inputs to clustering algorithms and aids forinterpreting the results of cluster analysis An exploration of some new techniques of summarization andexposure New graphical methods for assessing the separations among theeigenvalues of a correlation matrix and for comparing sets ofeigenvectors Knowledge gained from advances in robust estimation anddistributional models that are slightly broader than themultivariate normal This Second Edition is invaluable for graduate students, appliedstatisticians, engineers, and scientists wishing to usemultivariate techniques in a variety of disciplines.

Numerical Methods for Stochastic Processes

Author: Nicolas Bouleau
Publisher: John Wiley & Sons
ISBN: 0471546410
Release Date: 1994
Genre: Mathematics

In recent years, random variables and stochastic processes have emerged as important factors in predicting outcomes in virtually every field of applied and social science. Ironically, according to Nicolas Bouleau and Dominique Lepingle, the presence of randomness in the model sometimes leads engineers to accept crude mathematical treatments that produce inaccurate results. The purpose of Numerical Methods for Stochastic Processes is to add greater rigor to numerical treatment of stochastic processes so that they produce results that can be relied upon when making decisions and assessing risks. Based on a postgraduate course given by the authors at Paris 6 University, the text emphasizes simulation methods, which can now be implemented with specialized computer programs. Specifically presented are the Monte Carlo and shift methods, which use an "imitation of randomness" and have a wide range of applications, and the so-called quasi-Monte Carlo methods, which are rigorous but less widely applicable. Offering a broad introduction to the field, this book presents the current state of the main methods and ideas and the cases for which they have been proved. Nevertheless, the authors do explore problems raised by these newer methods and suggest areas in which further research is needed. Extensive notes and a full bibliography give interested readers the option of delving deeper into stochastic numerical analysis. For professional statisticians, engineers, and physical and social scientists, Numerical Methods for Stochastic Processes provides both the theoretical background and the necessary practical tools to improve predictions based on randomness in the model. With its exercises andbroad-spectrum coverage, it is also an excellent textbook for introductory graduate-level courses in stochastic process mathematics.

Multivariate Density Estimation

Author: David W. Scott
Publisher: John Wiley & Sons
ISBN: 0471547700
Release Date: 1992-08-31
Genre: Mathematics

Representation and geometry of multivariate data; Nonparametric estimation criteria; Histograms: theory and practice; Frequency polygons; Averaged shifted histograms; Kernel density estimators; The curse of dimensionality and dimension reduction; Nonparametric regression and additive models; Other applications.

Alternative Methods of Regression

Author: David Birkes
Publisher: John Wiley & Sons
ISBN: 9781118150245
Release Date: 2011-09-20
Genre: Mathematics

Of related interest. Nonlinear Regression Analysis and its Applications Douglas M. Bates and Donald G. Watts ".an extraordinary presentation of concepts and methods concerning the use and analysis of nonlinear regression models.highly recommend[ed].for anyone needing to use and/or understand issues concerning the analysis of nonlinear regression models." --Technometrics This book provides a balance between theory and practice supported by extensive displays of instructive geometrical constructs. Numerous in-depth case studies illustrate the use of nonlinear regression analysis--with all data sets real. Topics include: multi-response parameter estimation; models defined by systems of differential equations; and improved methods for presenting inferential results of nonlinear analysis. 1988 (0-471-81643-4) 365 pp. Nonlinear Regression G. A. F. Seber and C. J. Wild ".[a] comprehensive and scholarly work.impressively thorough with attention given to every aspect of the modeling process." --Short Book Reviews of the International Statistical Institute In this introduction to nonlinear modeling, the authors examine a wide range of estimation techniques including least squares, quasi-likelihood, and Bayesian methods, and discuss some of the problems associated with estimation. The book presents new and important material relating to the concept of curvature and its growing role in statistical inference. It also covers three useful classes of models --growth, compartmental, and multiphase --and emphasizes the limitations involved in fitting these models. Packed with examples and graphs, it offers statisticians, statistical consultants, and statistically oriented research scientists up-to-date access to their fields. 1989 (0-471-61760-1) 768 pp. Mathematical Programming in Statistics T. S. Arthanari and Yadolah Dodge "The authors have achieved their stated intention.in an outstanding and useful manner for both students and researchers.Contains a superb synthesis of references linked to the special topics and formulations by a succinct set of bibliographical notes.Should be in the hands of all system analysts and computer system architects." --Computing Reviews This unique book brings together most of the available results on applications of mathematical programming in statistics, and also develops the necessary statistical and programming theory and methods. 1981 (0-471-08073-X) 413 pp.

Statistical intervals

Author: Gerald J. Hahn
Publisher: Wiley-Interscience
ISBN: UOM:39015022043270
Release Date: 1991-09-02
Genre: Business & Economics

Presents a detailed exposition of statistical intervals and emphasizes applications in industry. The discussion differentiates at an elementary level among different kinds of statistical intervals and gives instruction with numerous examples and simple math on how to construct such intervals from sample data. This includes confidence intervals to contain a population percentile, confidence intervals on probability of meeting specified threshold value, and prediction intervals to include observation in a future sample. Also has an appendix containing computer subroutines for nonparametric statistical intervals.

Statistical Applications Using Fuzzy Sets

Author: Kenneth G. Manton
Publisher: Wiley-Interscience
ISBN: UOM:39015032989330
Release Date: 1994
Genre: Mathematics

Now there's a third approach using a new strategy for resolving measure theoretic issues involving this type of data. That approach centers on the fuzzy set or fuzzy partition models generated by convex geometrical sets. Originally developed in electrical engineering, these models have been finding a growing number of applications in computer science, physics, and theoretical biology. This popularity stems from the power of fuzzy set models to vastly improve on the approximation of the infinite dimensionality and heterogeneity of the real world that arises from the use of statistical partitions, no matter how fine.

Probability and statistical inference

Author: Robert Bartoszyński
Publisher: Wiley-Interscience
ISBN: UOM:39015037819144
Release Date: 1996-08-17
Genre: Business & Economics

Understanding the "why" of statistics and probabilityâa unique and useful emphasis on theory This outstanding textbook emphasizes theoretical comprehension rather than the narrow acquisition of concepts or skills. Probability and Statistical Inference focuses on the development of intuition and understanding through diversity of experience. This thought-provoking text reintroduces mathematics, abstractions, and theory into the study of statistics and probability, and demonstrates that greater abstraction leads to a wider applicability of the methods under discussion. Its unique approach to exercises integrates the knowledge gained here and promotes a more complete understanding of the material. Probability and Statistical Inference features: A wealth of examples illustrating concepts, theorems, and methodsâfrom numerical data and details of calculations, to ideas behind some of the methods, and more Accessible, user-friendly treatments that clearly explain concepts and motivations while pointing out pitfalls and difficulties of arguments A selection of advanced topics for students who would benefit from more thorough explanations An instructor's manual with solutions available from the publisher Suitable for upper-level undergraduate and graduate courses in statistics, and as a professional reference, this unparalleled volume offers useful insights to anyone who uses statistical tools, whatever the discipline. An Instructor's Manual presenting detailed solutions to all the problems in the book is available from the Wiley editorial department.

Operational subjective statistical methods

Author: Frank Lad
Publisher: Wiley-Interscience
ISBN: 0471143294
Release Date: 1996-09-27
Genre: Business & Economics

The mathematical implications of personal beliefs and values in science and commerce Amid a worldwide resurgence of interest in subjectivist statistical method, this book offers a fresh look at the role of personal judgments in statistical analysis. Frank Lad demonstrates how philosophical attention to meaning provides a sensible assessment of the prospects and procedures of empirical inferential learning. Operational Subjective Statistical Methods offers a systematic investigation of Bruno de Finetti's theory of probability and logic of uncertainty, which recognizes probability as the measure of personal uncertainty at the heart of its mathematical presentation. It identifies de Finetti's "fundamental theorem of coherent provision" as the unifying structure of probabilistic logic, and highlights the judgment of exchangeability rather than causal independence as the key probabilistic component of statistical inference. Broad in scope, yet firmly grounded in mathematical detail, this text/reference Invites readers to address the subjective personalist meaning of probability as motivating the mathematical construction * Contains numerous examples and problems, including computing problems using Matlab, assuming no background in Matlab * Explains how to use the material in three distinct sequential courses in math and statistics, as well as in courses at the graduate level in applied fields * Provides an introductory basis for understanding more complex structures of statistical analysis Complete with fifty illustrations, Operational Subjective Statistical Methods makes an intriguing discipline accessible to professionals, students, and the interested general reader. It contains a wealth of teaching and research material, and offers profound insight into the relationship between philosophy, faith, and scientific method.

Statistical Inference for Branching Processes

Author: Peter Guttorp
Publisher: Wiley-Interscience
ISBN: UOM:39015021518686
Release Date: 1991-08-19
Genre: Mathematics

An examination of the difficulties that statistical theory and, in particular, estimation theory can encounter within the area of dependent data. This is achieved through the study of the theory of branching processes starting with the demographic question: what is the probability that a family name becomes extinct? Contains observations on the generation sizes of the Bienaym?-Galton-Watson (BGW) process. Various parameters are estimated and branching process theory is contrasted to a Bayesian approach. Illustrations of branching process theory applications are shown for particular problems.

Forecasting with Dynamic Regression Models

Author: Alan Pankratz
Publisher: Wiley-Interscience
ISBN: UOM:39015024799069
Release Date: 1991-10-24
Genre: Mathematics

One of the most widely used tools in statistical forecasting, single equation regression models is examined here. A companion to the author's earlier work, Forecasting with Univariate Box-Jenkins Models: Concepts and Cases, the present text pulls together recent time series ideas and gives special attention to possible intertemporal patterns, distributed lag responses of output to input series and the auto correlation patterns of regression disturbance. It also includes six case studies.

Regression analysis by example

Author: Samprit Chatterjee
Publisher: Wiley-Interscience
ISBN: 0471884790
Release Date: 1991
Genre: Mathematics

A variety of ideas and methods of regression analysis are explored with the aid of realistic examples that highlight the analysis of data and include irregularities similar to those encountered in practice. Recent advances in regression diagnostics are covered with emphasis on plots such as component plus residual, added variable, sequence, along with index plots for leverage and function. The authors utilize standard and some not so standard summary statistics on the basis of their intuitive appeal to demonstrate concepts. The majority of analyses described are available in software packages on the market today.

Modern regression methods

Author: Thomas P. Ryan
Publisher: Wiley-Interscience
ISBN: 0471529125
Release Date: 1997
Genre: Business & Economics

The most comprehensive book available on state-of-the-art regression methodology, complete with exercises and solutions This combination book and disk set presents the full range of regression techniques available today to practitioners, researchers, and students of this popular and ever-changing field. Featuring a strong data analysis orientation and a more comprehensive treatment of regression diagnostics than is found in other texts, Modern Regression Methods contains a wealth of material assembled here for the first time, including recently developed techniques and some new methods introduced by the author, as well as fresh approaches to standard concepts. With thorough analyses of real-world data sets and many exercises with worked solutions, this unique resource reinforces learning while providing you with crucial hands-on experience in the practical application of skills. The book offers: * In-depth treatment of standard regression methods, including diagnostics, transformations, ridge regression, and variable selection techniques * A detailed examination of nonlinear regression, robust regression, and logistic regression, including both exact and maximum likelihood approaches for logistic regression * New graphical techniques and transformation strategies for multiple regression and a survey of nonparametric regression * Experimental designs for regression * Minitab macros to facilitate understanding and use of many of the new methods that are presented Amstat News asked three review editors to rate their top five favorite books in the September 2003 issue. Modern Regression Methods was among those chosen.