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Author: Tailen Hsing
Publisher: John Wiley & Sons
ISBN: 1118762568
Category : Mathematics
Languages : en
Pages : 368
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Book Description
Theoretical Foundations of Functional Data Analysis, with an Introduction to Linear Operators provides a uniquely broad compendium of the key mathematical concepts and results that are relevant for the theoretical development of functional data analysis (FDA). The self–contained treatment of selected topics of functional analysis and operator theory includes reproducing kernel Hilbert spaces, singular value decomposition of compact operators on Hilbert spaces and perturbation theory for both self–adjoint and non self–adjoint operators. The probabilistic foundation for FDA is described from the perspective of random elements in Hilbert spaces as well as from the viewpoint of continuous time stochastic processes. Nonparametric estimation approaches including kernel and regularized smoothing are also introduced. These tools are then used to investigate the properties of estimators for the mean element, covariance operators, principal components, regression function and canonical correlations. A general treatment of canonical correlations in Hilbert spaces naturally leads to FDA formulations of factor analysis, regression, MANOVA and discriminant analysis. This book will provide a valuable reference for statisticians and other researchers interested in developing or understanding the mathematical aspects of FDA. It is also suitable for a graduate level special topics course.
Author: Tailen Hsing
Publisher: John Wiley & Sons
ISBN: 1118762568
Category : Mathematics
Languages : en
Pages : 368
Get Book Here
Book Description
Theoretical Foundations of Functional Data Analysis, with an Introduction to Linear Operators provides a uniquely broad compendium of the key mathematical concepts and results that are relevant for the theoretical development of functional data analysis (FDA). The self–contained treatment of selected topics of functional analysis and operator theory includes reproducing kernel Hilbert spaces, singular value decomposition of compact operators on Hilbert spaces and perturbation theory for both self–adjoint and non self–adjoint operators. The probabilistic foundation for FDA is described from the perspective of random elements in Hilbert spaces as well as from the viewpoint of continuous time stochastic processes. Nonparametric estimation approaches including kernel and regularized smoothing are also introduced. These tools are then used to investigate the properties of estimators for the mean element, covariance operators, principal components, regression function and canonical correlations. A general treatment of canonical correlations in Hilbert spaces naturally leads to FDA formulations of factor analysis, regression, MANOVA and discriminant analysis. This book will provide a valuable reference for statisticians and other researchers interested in developing or understanding the mathematical aspects of FDA. It is also suitable for a graduate level special topics course.
Author: Katie Harron
Publisher: John Wiley & Sons
ISBN: 1119072468
Category : Medical
Languages : en
Pages : 288
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Book Description
A comprehensive compilation of new developments in data linkage methodology The increasing availability of large administrative databases has led to a dramatic rise in the use of data linkage, yet the standard texts on linkage are still those which describe the seminal work from the 1950-60s, with some updates. Linkage and analysis of data across sources remains problematic due to lack of discriminatory and accurate identifiers, missing data and regulatory issues. Recent developments in data linkage methodology have concentrated on bias and analysis of linked data, novel approaches to organising relationships between databases and privacy-preserving linkage. Methodological Developments in Data Linkage brings together a collection of contributions from members of the international data linkage community, covering cutting edge methodology in this field. It presents opportunities and challenges provided by linkage of large and often complex datasets, including analysis problems, legal and security aspects, models for data access and the development of novel research areas. New methods for handling uncertainty in analysis of linked data, solutions for anonymised linkage and alternative models for data collection are also discussed. Key Features: Presents cutting edge methods for a topic of increasing importance to a wide range of research areas, with applications to data linkage systems internationally Covers the essential issues associated with data linkage today Includes examples based on real data linkage systems, highlighting the opportunities, successes and challenges that the increasing availability of linkage data provides Novel approach incorporates technical aspects of both linkage, management and analysis of linked data This book will be of core interest to academics, government employees, data holders, data managers, analysts and statisticians who use administrative data. It will also appeal to researchers in a variety of areas, including epidemiology, biostatistics, social statistics, informatics, policy and public health.
Author: Benjamin Kedem
Publisher: John Wiley & Sons
ISBN: 0471461687
Category : Mathematics
Languages : en
Pages : 361
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Book Description
A thorough review of the most current regression methods in time series analysis Regression methods have been an integral part of time series analysis for over a century. Recently, new developments have made major strides in such areas as non-continuous data where a linear model is not appropriate. This book introduces the reader to newer developments and more diverse regression models and methods for time series analysis. Accessible to anyone who is familiar with the basic modern concepts of statistical inference, Regression Models for Time Series Analysis provides a much-needed examination of recent statistical developments. Primary among them is the important class of models known as generalized linear models (GLM) which provides, under some conditions, a unified regression theory suitable for continuous, categorical, and count data. The authors extend GLM methodology systematically to time series where the primary and covariate data are both random and stochastically dependent. They introduce readers to various regression models developed during the last thirty years or so and summarize classical and more recent results concerning state space models. To conclude, they present a Bayesian approach to prediction and interpolation in spatial data adapted to time series that may be short and/or observed irregularly. Real data applications and further results are presented throughout by means of chapter problems and complements. Notably, the book covers: * Important recent developments in Kalman filtering, dynamic GLMs, and state-space modeling * Associated computational issues such as Markov chain, Monte Carlo, and the EM-algorithm * Prediction and interpolation * Stationary processes
Author: Ronald R. Hocking
Publisher: John Wiley & Sons
ISBN: 0471458627
Category : Mathematics
Languages : en
Pages : 773
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Book Description
A popular statistical text now updated and better than ever! The ready availability of high-speed computers and statistical software encourages the analysis of ever larger and more complex problems while at the same time increasing the likelihood of improper usage. That is why it is increasingly important to educate end users in the correct interpretation of the methodologies involved. Now in its second edition, Methods and Applications of Linear Models: Regression and the Analysis of Variance seeks to more effectively address the analysis of such models through several important changes. Notable in this new edition: Fully updated and expanded text reflects the most recent developments in the AVE method Rearranged and reorganized discussions of application and theory enhance text’s effectiveness as a teaching tool More than 100 new exercises in the areas of regression and analysis of variance As in the First Edition, the author presents a thorough treatment of the concepts and methods of linear model analysis, and illustrates them with various numerical and conceptual examples, using a data-based approach to development and analysis. Data sets, available on an FTP site, allow readers to apply analytical methods discussed in the book.
Author: William F. Rosenberger
Publisher: John Wiley & Sons
ISBN: 0471654078
Category : Mathematics
Languages : en
Pages : 286
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Book Description
A unique overview that melds the concepts of conditionalprobability and stochastic processes into real-lifeapplications The role of randomization techniques in clinical trials has becomeincreasingly important. This comprehensive guide combines both theapplied aspects of randomization in clinical trials with aprobabilistic treatment of properties of randomization. Taking anunabashedly non-Bayesian and nonparametric approach to inference,the book focuses on the linear rank test under a randomizationmodel, with added discussion on likelihood-based inference as itrelates to sufficiency and ancillarity. Developments in stochasticprocesses and applied probability are also given where appropriate.Intuition is stressed over mathematics, but not without a cleardevelopment of the latter in the context of the former. Providing a consolidated review of the field, the book includesrelevant and practical discussions of: * The benefits of randomization in terms of reduction of bias * Randomization as a basis for inference * Covariate-adaptive and response-adaptive randomization * Current philosophies, controversies, and new developments With ample problem sets, theoretical exercises, and short computersimulations using SAS, Randomization in Clinical Trials: Theory andPractice is equally useful as a standard textbook in biostatisticsgraduate programs as well as a reliable reference forbiostatisticians in practice.
Author: James R. Thompson
Publisher: John Wiley & Sons
ISBN: 0470317906
Category : Mathematics
Languages : en
Pages : 332
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Book Description
A unique, integrated treatment of computer modeling and simulation "The future of science belongs to those willing to make the shift to simulation-based modeling," predicts Rice Professor James Thompson, a leading modeler and computational statistician widely known for his original ideas and engaging style. He discusses methods, available to anyone with a fast desktop computer, for integrating simulation into the modeling process in order to create meaningful models of real phenomena. Drawing from a wealth of experience, he gives examples from trading markets, oncology, epidemiology, statistical process control, physics, public policy, combat, real-world optimization, Bayesian analyses, and population dynamics. Dr. Thompson believes that, so far from liberating us from the necessity of modeling, the fast computer enables us to engage in realistic models of processes in , for example, economics, which have not been possible earlier because simple stochastic models in the forward temporal direction generally become quite unmanageably complex when one is looking for such things as likelihoods. Thompson shows how simulation may be used to bypass the necessity of obtaining likelihood functions or moment-generating functions as a precursor to parameter estimation. Simulation: A Modeler's Approach is a provocative and practical guide for professionals in applied statistics as well as engineers, scientists, computer scientists, financial analysts, and anyone with an interest in the synergy between data, models, and the digital computer.
Author: Shelemyahu Zacks
Publisher: John Wiley & Sons
ISBN: 1118605837
Category : Mathematics
Languages : en
Pages : 499
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Book Description
Provides the necessary skills to solve problems in mathematical statistics through theory, concrete examples, and exercises With a clear and detailed approach to the fundamentals of statistical theory, Examples and Problems in Mathematical Statistics uniquely bridges the gap between theory andapplication and presents numerous problem-solving examples that illustrate the relatednotations and proven results. Written by an established authority in probability and mathematical statistics, each chapter begins with a theoretical presentation to introduce both the topic and the important results in an effort to aid in overall comprehension. Examples are then provided, followed by problems, and finally, solutions to some of the earlier problems. In addition, Examples and Problems in Mathematical Statistics features: Over 160 practical and interesting real-world examples from a variety of fields including engineering, mathematics, and statistics to help readers become proficient in theoretical problem solving More than 430 unique exercises with select solutions Key statistical inference topics, such as probability theory, statistical distributions, sufficient statistics, information in samples, testing statistical hypotheses, statistical estimation, confidence and tolerance intervals, large sample theory, and Bayesian analysis Recommended for graduate-level courses in probability and statistical inference, Examples and Problems in Mathematical Statistics is also an ideal reference for applied statisticians and researchers.
Author: Peter Congdon
Publisher: John Wiley & Sons
ISBN: 1118895053
Category : Mathematics
Languages : en
Pages : 464
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Book Description
This book provides an accessible approach to Bayesian computing and data analysis, with an emphasis on the interpretation of real data sets. Following in the tradition of the successful first edition, this book aims to make a wide range of statistical modeling applications accessible using tested code that can be readily adapted to the reader's own applications. The second edition has been thoroughly reworked and updated to take account of advances in the field. A new set of worked examples is included. The novel aspect of the first edition was the coverage of statistical modeling using WinBUGS and OPENBUGS. This feature continues in the new edition along with examples using R to broaden appeal and for completeness of coverage.
Author: Takeaki Kariya
Publisher: John Wiley & Sons
ISBN: 0470866985
Category : Mathematics
Languages : en
Pages : 312
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Book Description
Generalised Least Squares adopts a concise and mathematically rigorous approach. It will provide an up-to-date self-contained introduction to the unified theory of generalized least squares estimations, adopting a concise and mathematically rigorous approach. The book covers in depth the 'lower and upper bounds approach', pioneered by the first author, which is widely regarded as a very powerful and useful tool for generalized least squares estimation, helping the reader develop their understanding of the theory. The book also contains exercises at the end of each chapter and applications to statistics, econometrics, and biometrics, enabling use for self-study or as a course text.
Author: Charles E. McCulloch
Publisher: John Wiley & Sons
ISBN: 0471654043
Category : Social Science
Languages : en
Pages : 358
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Book Description
Wiley Series in Probability and Statistics A modern perspective on mixed models The availability of powerful computing methods in recent decades has thrust linear and nonlinear mixed models into the mainstream of statistical application. This volume offers a modern perspective on generalized, linear, and mixed models, presenting a unified and accessible treatment of the newest statistical methods for analyzing correlated, nonnormally distributed data. As a follow-up to Searle's classic, Linear Models, and Variance Components by Searle, Casella, and McCulloch, this new work progresses from the basic one-way classification to generalized linear mixed models. A variety of statistical methods are explained and illustrated, with an emphasis on maximum likelihood and restricted maximum likelihood. An invaluable resource for applied statisticians and industrial practitioners, as well as students interested in the latest results, Generalized, Linear, and Mixed Models features: * A review of the basics of linear models and linear mixed models * Descriptions of models for nonnormal data, including generalized linear and nonlinear models * Analysis and illustration of techniques for a variety of real data sets * Information on the accommodation of longitudinal data using these models * Coverage of the prediction of realized values of random effects * A discussion of the impact of computing issues on mixed models
