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Author: John F. Monahan Publisher: Cambridge University Press ISBN: 1139498002 Category : Computers Languages : en Pages : 465
Book Description
This book explains how computer software is designed to perform the tasks required for sophisticated statistical analysis. For statisticians, it examines the nitty-gritty computational problems behind statistical methods. For mathematicians and computer scientists, it looks at the application of mathematical tools to statistical problems. The first half of the book offers a basic background in numerical analysis that emphasizes issues important to statisticians. The next several chapters cover a broad array of statistical tools, such as maximum likelihood and nonlinear regression. The author also treats the application of numerical tools; numerical integration and random number generation are explained in a unified manner reflecting complementary views of Monte Carlo methods. Each chapter contains exercises that range from simple questions to research problems. Most of the examples are accompanied by demonstration and source code available from the author's website. New in this second edition are demonstrations coded in R, as well as new sections on linear programming and the Nelder–Mead search algorithm.
Author: John F. Monahan Publisher: Cambridge University Press ISBN: 1139498002 Category : Computers Languages : en Pages : 465
Book Description
This book explains how computer software is designed to perform the tasks required for sophisticated statistical analysis. For statisticians, it examines the nitty-gritty computational problems behind statistical methods. For mathematicians and computer scientists, it looks at the application of mathematical tools to statistical problems. The first half of the book offers a basic background in numerical analysis that emphasizes issues important to statisticians. The next several chapters cover a broad array of statistical tools, such as maximum likelihood and nonlinear regression. The author also treats the application of numerical tools; numerical integration and random number generation are explained in a unified manner reflecting complementary views of Monte Carlo methods. Each chapter contains exercises that range from simple questions to research problems. Most of the examples are accompanied by demonstration and source code available from the author's website. New in this second edition are demonstrations coded in R, as well as new sections on linear programming and the Nelder–Mead search algorithm.
Author: George A. F. Seber Publisher: John Wiley & Sons ISBN: 0471725307 Category : Mathematics Languages : en Pages : 800
Book Description
WILEY-INTERSCIENCE PAPERBACK SERIES The Wiley-Interscience Paperback Series consists of selected books that have been made more accessible to consumers in an effort to increase global appeal and general circulation. With these new unabridged softcover volumes, Wiley hopes to extend the lives of these works by making them available to future generations of statisticians, mathematicians, and scientists. From the Reviews of Nonlinear Regression "A very good book and an important one in that it is likely to become a standard reference for all interested in nonlinear regression; and I would imagine that any statistician concerned with nonlinear regression would want a copy on his shelves." –The Statistician "Nonlinear Regression also includes a reference list of over 700 entries. The compilation of this material and cross-referencing of it is one of the most valuable aspects of the book. Nonlinear Regression can provide the researcher unfamiliar with a particular specialty area of nonlinear regression an introduction to that area of nonlinear regression and access to the appropriate references . . . Nonlinear Regression provides by far the broadest discussion of nonlinear regression models currently available and will be a valuable addition to the library of anyone interested in understanding and using such models including the statistical researcher." –Mathematical Reviews
Author: H. J. Bierens Publisher: Springer Science & Business Media ISBN: 3642455298 Category : Mathematics Languages : en Pages : 211
Book Description
This Lecture Note deals with asymptotic properties, i.e. weak and strong consistency and asymptotic normality, of parameter estimators of nonlinear regression models and nonlinear structural equations under various assumptions on the distribution of the data. The estimation methods involved are nonlinear least squares estimation (NLLSE), nonlinear robust M-estimation (NLRME) and non linear weighted robust M-estimation (NLWRME) for the regression case and nonlinear two-stage least squares estimation (NL2SLSE) and a new method called minimum information estimation (MIE) for the case of structural equations. The asymptotic properties of the NLLSE and the two robust M-estimation methods are derived from further elaborations of results of Jennrich. Special attention is payed to the comparison of the asymptotic efficiency of NLLSE and NLRME. It is shown that if the tails of the error distribution are fatter than those of the normal distribution NLRME is more efficient than NLLSE. The NLWRME method is appropriate if the distributions of both the errors and the regressors have fat tails. This study also improves and extends the NL2SLSE theory of Amemiya. The method involved is a variant of the instrumental variables method, requiring at least as many instrumental variables as parameters to be estimated. The new MIE method requires less instrumental variables. Asymptotic normality can be derived by employing only one instrumental variable and consistency can even be proved with out using any instrumental variables at all.
Author: Takeshi Amemiya Publisher: Harvard University Press ISBN: 0674251954 Category : Business & Economics Languages : en Pages : 540
Book Description
Advanced Econometrics is both a comprehensive text for graduate students and a reference work for econometricians. It will also be valuable to those doing statistical analysis in the other social sciences. Its main features are a thorough treatment of cross-section models, including qualitative response models, censored and truncated regression models, and Markov and duration models, as well as a rigorous presentation of large sample theory, classical least-squares and generalized least-squares theory, and nonlinear simultaneous equation models. Although the treatment is mathematically rigorous, the author has employed the theorem-proof method with simple, intuitively accessible assumptions. This enables readers to understand the basic structure of each theorem and to generalize it for themselves depending on their needs and abilities. Many simple applications of theorems are given either in the form of examples in the text or as exercises at the end of each chapter in order to demonstrate their essential points.
Author: Hossein Riazoshams Publisher: John Wiley & Sons ISBN: 1119010454 Category : Mathematics Languages : en Pages : 261
Book Description
The first book to discuss robust aspects of nonlinear regression—with applications using R software Robust Nonlinear Regression: with Applications using R covers a variety of theories and applications of nonlinear robust regression. It discusses both parts of the classic and robust aspects of nonlinear regression and focuses on outlier effects. It develops new methods in robust nonlinear regression and implements a set of objects and functions in S-language under SPLUS and R software. The software covers a wide range of robust nonlinear fitting and inferences, and is designed to provide facilities for computer users to define their own nonlinear models as an object, and fit models using classic and robust methods as well as detect outliers. The implemented objects and functions can be applied by practitioners as well as researchers. The book offers comprehensive coverage of the subject in 9 chapters: Theories of Nonlinear Regression and Inference; Introduction to R; Optimization; Theories of Robust Nonlinear Methods; Robust and Classical Nonlinear Regression with Autocorrelated and Heteroscedastic errors; Outlier Detection; R Packages in Nonlinear Regression; A New R Package in Robust Nonlinear Regression; and Object Sets. The first comprehensive coverage of this field covers a variety of both theoretical and applied topics surrounding robust nonlinear regression Addresses some commonly mishandled aspects of modeling R packages for both classical and robust nonlinear regression are presented in detail in the book and on an accompanying website Robust Nonlinear Regression: with Applications using R is an ideal text for statisticians, biostatisticians, and statistical consultants, as well as advanced level students of statistics.
Author: George G. Judge Publisher: John Wiley & Sons ISBN: 047189530X Category : Business & Economics Languages : en Pages : 1062
Book Description
This broadly based graduate-level textbook covers the major models and statistical tools currently used in the practice of econometrics. It examines the classical, the decision theory, and the Bayesian approaches, and contains material on single equation and simultaneous equation econometric models. Includes an extensive reference list for each topic.
Author: Peter J. Huber Publisher: SIAM ISBN: 9781611970036 Category : Mathematics Languages : en Pages : 77
Book Description
Here is a brief, well-organized, and easy-to-follow introduction and overview of robust statistics. Huber focuses primarily on the important and clearly understood case of distribution robustness, where the shape of the true underlying distribution deviates slightly from the assumed model (usually the Gaussian law). An additional chapter on recent developments in robustness has been added and the reference list has been expanded and updated from the 1977 edition.
Author: Andrej Pázman Publisher: Springer Science & Business Media ISBN: 9401724504 Category : Mathematics Languages : en Pages : 268
Book Description
Nonlinear statistical modelling is an area of growing importance. This monograph presents mostly new results and methods concerning the nonlinear regression model. Among the aspects which are considered are linear properties of nonlinear models, multivariate nonlinear regression, intrinsic and parameter effect curvature, algorithms for calculating the L2-estimator and both local and global approximation. In addition to this a chapter has been added on the large topic of nonlinear exponential families. The volume will be of interest to both experts in the field of nonlinear statistical modelling and to those working in the identification of models and optimization, as well as to statisticians in general.
Author: Raymond J. Carroll Publisher: CRC Press ISBN: 1420010131 Category : Mathematics Languages : en Pages : 484
Book Description
It's been over a decade since the first edition of Measurement Error in Nonlinear Models splashed onto the scene, and research in the field has certainly not cooled in the interim. In fact, quite the opposite has occurred. As a result, Measurement Error in Nonlinear Models: A Modern Perspective, Second Edition has been revamped and ex
Author: John F. Monahan
Author: John F. Monahan
Author: George A. F. Seber
Author: H. J. Bierens
Author: Takeshi Amemiya
Author: Hossein Riazoshams
Author: George G. Judge
Author: Jian Yang
Author: Peter J. Huber
Author: Andrej Pázman
Author: Raymond J. Carroll