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Author: John Hanfelt
Publisher: Chapman & Hall/CRC
ISBN: 9781420067606
Category : Mathematics
Languages : en
Pages : 250
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Book Description
From the fully parametric setting to the semiparametric setting, General Estimating Function Theoryprovides a comprehensive introduction to the increasingly popular theory of estimating functions, which offers a unified framework for the study of many seemingly diverse methods of estimation. The book focuses on the significance of the modern theory rather than on mathematical rigor. It explores biostatistics topics, including artificial likelihoods, nuisance parameters, and model selection methods. The text also provides appendices on regularity conditions as well as Hilbert space and orthogonal projections.
Author: John Hanfelt
Publisher: Chapman & Hall/CRC
ISBN: 9781420067606
Category : Mathematics
Languages : en
Pages : 250
Get Book Here
Book Description
From the fully parametric setting to the semiparametric setting, General Estimating Function Theoryprovides a comprehensive introduction to the increasingly popular theory of estimating functions, which offers a unified framework for the study of many seemingly diverse methods of estimation. The book focuses on the significance of the modern theory rather than on mathematical rigor. It explores biostatistics topics, including artificial likelihoods, nuisance parameters, and model selection methods. The text also provides appendices on regularity conditions as well as Hilbert space and orthogonal projections.
Author: V. P. Godambe
Publisher: Oxford University Press on Demand
ISBN: 9780198522287
Category : History
Languages : en
Pages : 344
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Book Description
This volume comprises a comprehensive collection of original papers on the subject of estimating functions. It is intended to provide statisticians with an overview of both the theory and the applications of estimating functions in biostatistics, stochastic processes, and survey sampling. From the early 1960s when the concept of optimality criterion was first formulated, together with the later work on optimal estimating functions, this subject has become both an active research area in its own right and also a cornerstone of the modern theory of statistics. Individual chapters have been written by experts in their respective fields and as a result this volume will be an invaluable reference guide to this topic as well as providing an introduction to the area for non-experts.
Author: Parimal Mukhopadhyay
Publisher: Alpha Science Int'l Ltd.
ISBN: 9781842651636
Category : Business & Economics
Languages : en
Pages : 252
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Book Description
The theory of estimating functions plays a major role in analysis of data pertaining to Biostatistics, Econometrics, Time Series Analysis, Reliability studies and other varied fields. This book discusses at length the application of the theory in interpretation of results in Survey Sampling.
Author: L. Kubacek
Publisher: Elsevier
ISBN: 0444598081
Category : Mathematics
Languages : en
Pages : 335
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Book Description
The application of estimation theory renders the processing of experimental results both rational and effective, and thus helps not only to make our knowledge more precise but to determine the measure of its reliability. As a consequence, estimation theory is indispensable in the analysis of the measuring processes and of experiments in general.The knowledge necessary for studying this book encompasses the disciplines of probability and mathematical statistics as studied in the third or fourth year at university. For readers interested in applications, comparatively detailed chapters on linear and quadratic estimations, and normality of observation vectors have been included. Chapter 2 includes selected items of information from algebra, functional analysis and the theory of probability, intended to facilitate the reading of the text proper and to save the reader looking up individual theorems in various textbooks and papers; it is mainly devoted to the reproducing kernel Hilbert spaces, helpful in solving many estimation problems. The text proper of the book begins with Chapter 3. This is divided into two parts: the first deals with sufficient statistics, complete sufficient statistics, minimal sufficient statistics and relations between them; the second contains the mostimportant inequalities of estimation theory for scalar and vector valued parameters and presents properties of the exponential family of distributions.The fourth chapter is an introduction to asymptotic methods of estimation. The method of statistical moments and the maximum-likelihood method are investigated. The sufficient conditions for asymptotical normality of the estimators are given for both methods. The linear and quadratic methods of estimation are dealt with in the fifth chapter. The method of least squares estimation is treated. Five basic regular versions of the regression model and the unified linear model of estimation are described. Unbiased estimators for unit dispersion (factor of the covariance matrix) are given for all mentioned cases. The equivalence of the least-squares method to the method of generalized minimum norm inversion of the design matrix of the regression model is studied in detail. The problem of estimating the covariance components in the mixed model is mentioned as well. Statistical properties of linear and quadratic estimators developed in the fifth chapter in the case of normally distributed errors of measurement are given in Chapter 6. Further, the application of tensor products of Hilbert spaces generated by the covariance matrix of random error vector of observations is demonstrated. Chapter 7 reviews some further important methods of estimation theory. In the first part Wald's method of decision functions is applied to the construction of estimators. The method of contracted estimators and the method of Hoerl and Kennard are presented in the second part. The basic ideas of robustness and Bahadur's approach to estimation theory are presented in the third and fourth parts of this last chapter.
Author: Andreas Ziegler
Publisher: Springer Science & Business Media
ISBN: 1461404991
Category : Mathematics
Languages : en
Pages : 155
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Book Description
Generalized estimating equations have become increasingly popular in biometrical, econometrical, and psychometrical applications because they overcome the classical assumptions of statistics, i.e. independence and normality, which are too restrictive for many problems. Therefore, the main goal of this book is to give a systematic presentation of the original generalized estimating equations (GEE) and some of its further developments. Subsequently, the emphasis is put on the unification of various GEE approaches. This is done by the use of two different estimation techniques, the pseudo maximum likelihood (PML) method and the generalized method of moments (GMM). The author details the statistical foundation of the GEE approach using more general estimation techniques. The book could therefore be used as basis for a course to graduate students in statistics, biostatistics, or econometrics, and will be useful to practitioners in the same fields.
Author: James W. Hardin
Publisher: CRC Press
ISBN: 1439881146
Category : Mathematics
Languages : en
Pages : 277
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Book Description
Generalized Estimating Equations, Second Edition updates the best-selling previous edition, which has been the standard text on the subject since it was published a decade ago. Combining theory and application, the text provides readers with a comprehensive discussion of GEE and related models. Numerous examples are employed throughout the text, al
Author: Laszlo Matyas
Publisher: Cambridge University Press
ISBN: 9780521669672
Category : Business & Economics
Languages : en
Pages : 332
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Book Description
The generalized method of moments (GMM) estimation has emerged as providing a ready to use, flexible tool of application to a large number of econometric and economic models by relying on mild, plausible assumptions. The principal objective of this volume is to offer a complete presentation of the theory of GMM estimation as well as insights into the use of these methods in empirical studies. It is also designed to serve as a unified framework for teaching estimation theory in econometrics. Contributors to the volume include well-known authorities in the field based in North America, the UK/Europe, and Australia. The work is likely to become a standard reference for graduate students and professionals in economics, statistics, financial modeling, and applied mathematics.
Author: Jerry M. Mendel
Publisher: Pearson Education
ISBN: 0132440792
Category : Technology & Engineering
Languages : en
Pages : 891
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Book Description
Estimation theory is a product of need and technology. As a result, it is an integral part of many branches of science and engineering. To help readers differentiate among the rich collection of estimation methods and algorithms, this book describes in detail many of the important estimation methods and shows how they are interrelated. Written as a collection of lessons, this book introduces readers o the general field of estimation theory and includes abundant supplementary material.
Author: Vladimir Vapnik
Publisher: Springer Science & Business Media
ISBN: 1475732643
Category : Mathematics
Languages : en
Pages : 324
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Book Description
The aim of this book is to discuss the fundamental ideas which lie behind the statistical theory of learning and generalization. It considers learning as a general problem of function estimation based on empirical data. Omitting proofs and technical details, the author concentrates on discussing the main results of learning theory and their connections to fundamental problems in statistics. This second edition contains three new chapters devoted to further development of the learning theory and SVM techniques. Written in a readable and concise style, the book is intended for statisticians, mathematicians, physicists, and computer scientists.
Author: N. Balakrishnan
Publisher: CRC Press
ISBN: 9780203493205
Category : Mathematics
Languages : en
Pages : 562
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Book Description
At the International Indian Statistical Association Conference, held at McMaster University in Ontario, Canada, participants focused on advancements in theory and methodology of probability and statistics. This is one of two volumes containing invited papers from the meeting. The 32 chapters deal with different topics of interest, including stochastic processes and inference, distributions and characterizations, inference, Bayesian inference, selection methods, regression methods, and methods in health research. The text is ideal for applied mathematicians, statisticians, and researchers in the field.
