An Introduction to Estimating Functions PDF Download

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: Ishwar V. Basawa
Publisher: IMS
ISBN: 9780940600447
Category : Mathematics
Languages : en
Pages : 460

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Book Description

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: Christopher G. Small
Publisher: Oxford University Press
ISBN: 9780198506881
Category : Mathematics
Languages : en
Pages : 330

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Book Description
Non linearity arises in statistical inference in various ways, with varying degrees of severity, as an obstacle to statistical analysis. More entrenched forms of nonlinearity often require intensive numerical methods to construct estimators, and the use of root search algorithms, or one-step estimators, is a standard method of solution. This book provides a comprehensive study of nonlinear estimating equations and artificial likelihood's for statistical inference. It provides extensive coverage and comparison of hill climbing algorithms, which when started at points of nonconcavity often have very poor convergence properties, and for additional flexibility proposes a number of modification to the standard methods for solving these algorithms. The book also extends beyond simple root search algorithms to include a discussion of the testing of roots for consistency, and the modification of available estimating functions to provide greater stability in inference. A variety of examples from practical applications are included to illustrate the problems and possibilities thus making this text ideal for the research statistician and graduate student.

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: James W. Hardin
Publisher: CRC Press
ISBN: 1420035282
Category : Mathematics
Languages : en
Pages : 237

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Book Description
Although powerful and flexible, the method of generalized linear models (GLM) is limited in its ability to accurately deal with longitudinal and clustered data. Developed specifically to accommodate these data types, the method of Generalized Estimating Equations (GEE) extends the GLM algorithm to accommodate the correlated data encountered in heal

Author: Anil K. Bera
Publisher:
ISBN:
Category :
Languages : en
Pages : 0

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Book Description
The idea of using estimating functions goes a long way back, at least to Karl Pearson's introduction to the method of moment in 1894. It is now a very active area of research in the statistics literature. One aim of this chapter is to provide an account of the developments relating to the theory of estimating functions. Starting from the simple case of single parameter under independent set up, we cover the multi-parameter, presence of nuisance parameters and dependent data cases. Applications of the estimating function technique to econometrics is still at its infancy. However, we illustrate how this estimation approach could be used in various time series models, such as random coefficient, threshold, bilinear, autoregressive conditional heteroscedasticity models, also in spatial, longitudinal data and median regression analyses. The chapter is concluded with some remarks on the place of estimating function in the history of the statistical estimation techniques.

Author: Kevin Edward Burns
Publisher:
ISBN:
Category :
Languages : en
Pages : 156

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Book Description
In this dissertation, we consider the problem of estimating functions of parameters found in reliability and queueing models. The problem is to allocate a fixed sampling budget among the populations with the goal of minimizing the mean squared error (MSF) of the estimator. We consider the reliability model with three components such that the probability the system works is f(u1,u2,u3) = u1(u2+u3), and the mean waiting time of the M/G/I queue. For each of these models, we consider a set of sample sizes referred to as a first-allocation procedure which minimizes the first-order approximation to the MSE. Since the first-order allocation procedure depends on the unknown parameters in the model, we propose a two-stage procedure in which we first use a fraction of the sampling budget to estimate the unknown parameters and then allocate the remaining budget based on the initial sample. We show that the difference between the MSE for the two-stage procedure and the minimum MSE obtained using the optimal set of sample sizes from the first-allocation procedure goes to zero as the budget goes to infinity. Simulations are used to demonstrate the asymptotic optimality results for the two stage procedures. The empirical studies show that the two stage estimation procedures work well for reasonable sample sizes.

Author: James W. Hardin
Publisher: CRC Press
ISBN: 1439881138
Category : Mathematics
Languages : en
Pages : 280

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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, along with the software code used to create, run, and evaluate the models being examined. Stata is used as the primary software for running and displaying modeling output; associated R code is also given to allow R users to replicate Stata examples. Specific examples of SAS usage are provided in the final chapter as well as on the book’s website. This second edition incorporates comments and suggestions from a variety of sources, including the Statistics.com course on longitudinal and panel models taught by the authors. Other enhancements include an examination of GEE marginal effects; a more thorough presentation of hypothesis testing and diagnostics, covering competing hierarchical models; and a more detailed examination of previously discussed subjects. Along with doubling the number of end-of-chapter exercises, this edition expands discussion of various models associated with GEE, such as penalized GEE, cumulative and multinomial GEE, survey GEE, and quasi-least squares regression. It also offers a thoroughly new presentation of model selection procedures, including the introduction of an extension to the QIC measure that is applicable for choosing among working correlation structures. See Professor Hilbe discuss the book.