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Nonlinear Statistical Estimation With Numerical Maximum Likelihood
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Book Synopsis Nonlinear Statistical Estimation with Numerical Maximum Likelihood by : Gerald Gerard Brown
Download or read book Nonlinear Statistical Estimation with Numerical Maximum Likelihood written by Gerald Gerard Brown and published by . This book was released on 1974 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: The topics of maximum likelihood estimation and nonlinear programming are developed thoroughly with emphasis on the numerical details of obtaining estimates from highly nonlinear models. Parametric estimation is discussed with the three parameter Weibull family of densities serving as an example. A general nonlinear programming method is discussed for both first and second order representations of the maximum likelihood estimaton, as well as a hybrid of both approaches. A new class of constrained parametric estimators is introduced with numerical methods for their determination. Structural estimation with maximum likelihood is examined, and a Bernoulli regression technique is presented.
Book Synopsis Numerical Methods for Nonlinear Estimating Equations by : Christopher G. Small
Download or read book Numerical Methods for Nonlinear Estimating Equations written by Christopher G. Small and published by Oxford University Press. This book was released on 2003 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Nonlinear Estimation by : Gavin J.S. Ross
Download or read book Nonlinear Estimation written by Gavin J.S. Ross and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: Non-Linear Estimation is a handbook for the practical statistician or modeller interested in fitting and interpreting non-linear models with the aid of a computer. A major theme of the book is the use of 'stable parameter systems'; these provide rapid convergence of optimization algorithms, more reliable dispersion matrices and confidence regions for parameters, and easier comparison of rival models. The book provides insights into why some models are difficult to fit, how to combine fits over different data sets, how to improve data collection to reduce prediction variance, and how to program particular models to handle a full range of data sets. The book combines an algebraic, a geometric and a computational approach, and is illustrated with practical examples. A final chapter shows how this approach is implemented in the author's Maximum Likelihood Program, MLP.
Book Synopsis Maximum Likelihood Estimation and Inference by : Russell B. Millar
Download or read book Maximum Likelihood Estimation and Inference written by Russell B. Millar and published by John Wiley & Sons. This book was released on 2011-07-26 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book takes a fresh look at the popular and well-established method of maximum likelihood for statistical estimation and inference. It begins with an intuitive introduction to the concepts and background of likelihood, and moves through to the latest developments in maximum likelihood methodology, including general latent variable models and new material for the practical implementation of integrated likelihood using the free ADMB software. Fundamental issues of statistical inference are also examined, with a presentation of some of the philosophical debates underlying the choice of statistical paradigm. Key features: Provides an accessible introduction to pragmatic maximum likelihood modelling. Covers more advanced topics, including general forms of latent variable models (including non-linear and non-normal mixed-effects and state-space models) and the use of maximum likelihood variants, such as estimating equations, conditional likelihood, restricted likelihood and integrated likelihood. Adopts a practical approach, with a focus on providing the relevant tools required by researchers and practitioners who collect and analyze real data. Presents numerous examples and case studies across a wide range of applications including medicine, biology and ecology. Features applications from a range of disciplines, with implementation in R, SAS and/or ADMB. Provides all program code and software extensions on a supporting website. Confines supporting theory to the final chapters to maintain a readable and pragmatic focus of the preceding chapters. This book is not just an accessible and practical text about maximum likelihood, it is a comprehensive guide to modern maximum likelihood estimation and inference. It will be of interest to readers of all levels, from novice to expert. It will be of great benefit to researchers, and to students of statistics from senior undergraduate to graduate level. For use as a course text, exercises are provided at the end of each chapter.
Book Synopsis Maximum Likelihood Estimation with Stata, Fourth Edition by : William Gould
Download or read book Maximum Likelihood Estimation with Stata, Fourth Edition written by William Gould and published by Stata Press. This book was released on 2010-10-27 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: Maximum Likelihood Estimation with Stata, Fourth Edition is written for researchers in all disciplines who need to compute maximum likelihood estimators that are not available as prepackaged routines. Readers are presumed to be familiar with Stata, but no special programming skills are assumed except in the last few chapters, which detail how to add a new estimation command to Stata. The book begins with an introduction to the theory of maximum likelihood estimation with particular attention on the practical implications for applied work. Individual chapters then describe in detail each of the four types of likelihood evaluator programs and provide numerous examples, such as logit and probit regression, Weibull regression, random-effects linear regression, and the Cox proportional hazards model. Later chapters and appendixes provide additional details about the ml command, provide checklists to follow when writing evaluators, and show how to write your own estimation commands.
Book Synopsis Statistical Tools for Nonlinear Regression by : Sylvie Huet
Download or read book Statistical Tools for Nonlinear Regression written by Sylvie Huet and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt: Statistical Tools for Nonlinear Regression presents methods for analyzing data. It has been expanded to include binomial, multinomial and Poisson non-linear models. The examples are analyzed with the free software nls2 updated to deal with the new models included in the second edition. The nls2 package is implemented in S-PLUS and R. Several additional tools are included in the package for calculating confidence regions for functions of parameters or calibration intervals, using classical methodology or bootstrap.
Book Synopsis Maximum Likelihood Estimation of a Nonlinear System Dynamic Market Growth Model by : Sherif Rushdy
Download or read book Maximum Likelihood Estimation of a Nonlinear System Dynamic Market Growth Model written by Sherif Rushdy and published by . This book was released on 1981 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent efforts to determine the proper role of formal statistical estimation in modeling "System Dynamics" models show that the parameter estimates derived from Ordinary and Generalized Least Squares (OLS and GLS) are highly sensitive to errors in data measurement, and likely to prove misleading if used as a basis for selection of parameter values or structural analysis. Using the framework developed in this previous work, - where a nonlinear feedback model generates synthetic data, which is then used to estimate model parameters and thus provide a basis for the evaluation of an estimation technique, - this thesis reviews previous results with OLS and investigates alternative estimation techniques. A review of both econometric and engineering techniques, together with some preliminary experimental results revealed that no econometric estimation technique proved capable of meeting the requirements of the estimation of parameters in a nonlinear dynamic feedback model in the presence of measurement noise. The only promising method, the Filtering Form of the Maximum Likelihood algorithm, was found in the engineering literature where it is being used in a growing number of applications. A general FORTRAN program was developed to implement this algorithm and was tried out on three small-scale linear and nonlinear models. The method was found to be capable of drastically improving upon the Least Squares estimates, if sufficient Knowledge about the noise statistics (which present identifiability problems if they are all to be estimated) was available. However, experimentation on Forrester's "Market-Growth" model, while still modest in size compared to many System Dynamics models (nine equations and fifteen parameters to estimate), revealed the many limitations (in particular in convergence and cost) of this algorithm, that preclude its use in socio-economic applications. In the light of the above results, alternative methods of model validation, and in particular a more formal use of sensitivity testing, are suggested for further research.
Book Synopsis Numerical Methods of Statistics by : John F. Monahan
Download or read book Numerical Methods of Statistics written by John F. Monahan and published by Cambridge University Press. This book was released on 2011-04-18 with total page 465 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Nonlinear models in assessment in the social sciences: estimation by stochastic approximation, a frequentist mcmc by :
Download or read book Nonlinear models in assessment in the social sciences: estimation by stochastic approximation, a frequentist mcmc written by and published by . This book was released on 2004 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Neste trabalho apresentamos algumas contrubuições ao estudo dos modelosde avaliação estatística usados nas ciências sociais. As contribuiçõesoriginais são: i) uma descrição unificada sobre como a teoria da mediçãoevoluiu nas diversas disciplinas científicas; ii) uma resenha abrangente sobreos métodos de estimação por máxima verossimilhança empregados namedição estatística; iii) uma formulação geral do métodos da máxima verossimilhança tendo em vista a aplicação em modelos não-lineares; e principalmente, iv) a apresentação do método da aproximação estocástica naestimação dos modelos estatísticos de avaliação e medição. Os modelos não-lineares ocorrem freqüentemente nas ciências sociais ondeé importante a modelagem de variáveis de resposta dicotômicas ou ordinais. Em particular, este trabalho trata dos modelos da teoria da respostaao item, dos modelos de regressão logística e dos modelos de componentesaleatórias em geral. A estimação destes modelos ainda é objeto de intensapesquisa. Não se pode afirmar que exista um método de estimaçãointeiramente confiável. Os métodos aproximados produzem estimativas comviés acentuado nas componentes de variância, enquanto os métodos de integração numérica e os métodos bayesianos podem apresentar problemas deconvergência em muitos casos. O método da aproximação estocástica se baseiana maximização da verossimilhança e emprega o algoritmo de Robbins-Monro para resolver a equação do escore. Como um método estocástico elegera um processo de Markov que se aproxima das estimativas desejadas eportanto pode ser considerado um MCMC (Monte Carlo Markov chain)freqüentista. Nas simulações realizadas o método apresentou um bom desempenho, produzindo estimativas com viés pequeno, precisão razoável eraros problemas de convergência.
Book Synopsis Numerical Methods of Statistics by : John F. Monahan
Download or read book Numerical Methods of Statistics written by John F. Monahan and published by Cambridge University Press. This book was released on 2001-02-05 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 2001 book provides a basic background in numerical analysis and its applications in statistics.
Book Synopsis Statistical Inference in Non-Linear Models in Econometrics by : Theertham Gangaram
Download or read book Statistical Inference in Non-Linear Models in Econometrics written by Theertham Gangaram and published by LAP Lambert Academic Publishing. This book was released on 2013 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the present book, Chapter-I is an introductory one. It gives general introduction about the nonlinear regression models. A brief review about the existing inferential procedures for nonlinear regression models has been give in Chapter-II. It contains various nonlinear methods, of estimation based on nonlinear least squares and maximum likelihood methods, besides the methods by using some numerical analysis procedures.Chapter-II and IV describe the specification and estimation of some important nonlinear production function models such as Cobb-Douglas, Constant Elasticity of Substitution (CES), Variable Elasticity of Substitution (VES) and Transcedental Logarithmic (Translog) Production functions. Some new Inferential procedures for certain nonlinear regression models have been proposed and developed in Chapter V. The directions for further research along with the conclusions have been presented in Chapter-VI. General selected references regarding nonlinear regression models have been documented under Bibliography.
Book Synopsis Introduction to Multivariate Analysis by : Sadanori Konishi
Download or read book Introduction to Multivariate Analysis written by Sadanori Konishi and published by CRC Press. This book was released on 2014-06-06 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: Select the Optimal Model for Interpreting Multivariate Data Introduction to Multivariate Analysis: Linear and Nonlinear Modeling shows how multivariate analysis is widely used for extracting useful information and patterns from multivariate data and for understanding the structure of random phenomena. Along with the basic concepts of various procedures in traditional multivariate analysis, the book covers nonlinear techniques for clarifying phenomena behind observed multivariate data. It primarily focuses on regression modeling, classification and discrimination, dimension reduction, and clustering. The text thoroughly explains the concepts and derivations of the AIC, BIC, and related criteria and includes a wide range of practical examples of model selection and evaluation criteria. To estimate and evaluate models with a large number of predictor variables, the author presents regularization methods, including the L1 norm regularization that gives simultaneous model estimation and variable selection. For advanced undergraduate and graduate students in statistical science, this text provides a systematic description of both traditional and newer techniques in multivariate analysis and machine learning. It also introduces linear and nonlinear statistical modeling for researchers and practitioners in industrial and systems engineering, information science, life science, and other areas.
Book Synopsis Maximum likelihood estimation by means of nonlinear least squares by : Robert I. Jennrich
Download or read book Maximum likelihood estimation by means of nonlinear least squares written by Robert I. Jennrich and published by . This book was released on 1975 with total page 9 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Maximum-likelihood Prediction and Estimation for Nonlinear Dynamic Systems by : L. D. Attaway
Download or read book Maximum-likelihood Prediction and Estimation for Nonlinear Dynamic Systems written by L. D. Attaway and published by . This book was released on 1968 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt: A method is given for determining the system state using noise-corrupted observations of a non-linear dynamic invector process, with a numerical application to radar observation of a reentry body. The study examined the feasibility of numerically solving the vector-differential equations satisfied by the maximum-likelihood estimator. The maximum-likelihood estimate is that initial condition which minimizes a certain functional on itself, on the observation, and on the a priori statistics.
Book Synopsis Nonlinear Estimation and Classification by : David D. Denison
Download or read book Nonlinear Estimation and Classification written by David D. Denison and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 465 pages. Available in PDF, EPUB and Kindle. Book excerpt: Researchers in many disciplines face the formidable task of analyzing massive amounts of high-dimensional and highly-structured data. This is due in part to recent advances in data collection and computing technologies. As a result, fundamental statistical research is being undertaken in a variety of different fields. Driven by the complexity of these new problems, and fueled by the explosion of available computer power, highly adaptive, non-linear procedures are now essential components of modern "data analysis," a term that we liberally interpret to include speech and pattern recognition, classification, data compression and signal processing. The development of new, flexible methods combines advances from many sources, including approximation theory, numerical analysis, machine learning, signal processing and statistics. The proposed workshop intends to bring together eminent experts from these fields in order to exchange ideas and forge directions for the future.
Book Synopsis Econometric Modelling with Time Series by : Vance Martin
Download or read book Econometric Modelling with Time Series written by Vance Martin and published by Cambridge University Press. This book was released on 2012-12-28 with total page 924 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a general framework for specifying, estimating, and testing time series econometric models. Special emphasis is given to estimation by maximum likelihood, but other methods are also discussed, including quasi-maximum likelihood estimation, generalized method of moments estimation, nonparametric estimation, and estimation by simulation. An important advantage of adopting the principle of maximum likelihood as the unifying framework for the book is that many of the estimators and test statistics proposed in econometrics can be derived within a likelihood framework, thereby providing a coherent vehicle for understanding their properties and interrelationships. In contrast to many existing econometric textbooks, which deal mainly with the theoretical properties of estimators and test statistics through a theorem-proof presentation, this book squarely addresses implementation to provide direct conduits between the theory and applied work.
Book Synopsis Parameter Estimation in Engineering and Science by : James Vere Beck
Download or read book Parameter Estimation in Engineering and Science written by James Vere Beck and published by James Beck. This book was released on 1977 with total page 540 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to and survey of parameter estimation; Probability; Introduction to statistics; Parameter estimation methods; Introduction to linear estimation; Matrix analysis for linear parameter estimation; Minimization of sum of squares functions for models nonlinear in parameters; Design of optimal experiments.
