Download or read book Stochastic Approximation and Nonlinear Regression written by Arthur E. Albert and published by MIT Press (MA). This book was released on 2003-02-01 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph addresses the problem of "real-time" curve fitting in the presence of noise, from the computational and statistical viewpoints. It examines the problem of nonlinear regression, where observations are made on a time series whose mean-value function is known except for a vector parameter. In contrast to the traditional formulation, data are imagined to arrive in temporal succession. The estimation is carried out in real time so that, at each instant, the parameter estimate fully reflects all available data.Specifically, the monograph focuses on estimator sequences of the so-called differential correction type. The term "differential correction" refers to the fact that the difference between the components of the updated and previous estimators is proportional to the difference between the current observation and the value that would be predicted by the regression function if the previous estimate were in fact the true value of the unknown vector parameter. The vector of proportionality factors (which is generally time varying and can depend upon previous estimates) is called the "gain" or "smoothing" vector.The main purpose of this research is to relate the large-sample statistical behavior of such estimates (consistency, rate of convergence, large-sample distribution theory, asymptotic efficiency) to the properties of the regression function and the choice of smoothing vectors. Furthermore, consideration is given to the tradeoff that can be effected between computational simplicity and statistical efficiency through the choice of gains.Part I deals with the special cases of an unknown scalar parameter-discussing probability-one and mean-square convergence, rates of mean-square convergence, and asymptotic distribution theory of the estimators for various choices of the smoothing sequence. Part II examines the probability-one and mean-square convergence of the estimators in the vector case for various choices of smoothing vectors. Examples are liberally sprinkled throughout the book. Indeed, the last chapter is devoted entirely to the discussion of examples at varying levels of generality.If one views the stochastic approximation literature as a study in the asymptotic behavior of solutions to a certain class of nonlinear first-order difference equations with stochastic driving terms, then the results of this monograph also serve to extend and complement many of the results in that literature, which accounts for the authors' choice of title.The book is written at the first-year graduate level, although this level of maturity is not required uniformly. Certainly the reader should understand the concept of a limit both in the deterministic and probabilistic senses (i.e., almost sure and quadratic mean convergence). This much will assure a comfortable journey through the first fourth of the book. Chapters 4 and 5 require an acquaintance with a few selected central limit theorems. A familiarity with the standard techniques of large-sample theory will also prove useful but is not essential. Part II, Chapters 6 through 9, is couched in the language of matrix algebra, but none of the "classical" results used are deep. The reader who appreciates the elementary properties of eigenvalues, eigenvectors, and matrix norms will feel at home.MIT Press Research Monograph No. 42
Download or read book Stochastic Approximation and Nonlinear Regression by Arthur E Albert and Leland A Gardner written by Arthur E. Albert and published by . This book was released on 1967 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Stochastic Approximation and Recursive Algorithms and Applications written by Harold Kushner and published by Springer Science & Business Media. This book was released on 2006-05-04 with total page 485 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a thorough development of the modern theory of stochastic approximation or recursive stochastic algorithms for both constrained and unconstrained problems. This second edition is a thorough revision, although the main features and structure remain unchanged. It contains many additional applications and results as well as more detailed discussion.
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.
Download or read book On Stochastic Approximation written by Aryeh Dvoretsky and published by . This book was released on 1955 with total page 84 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Stochastic Approximation and Optimization of Random Systems written by L. Ljung and published by Birkhäuser. This book was released on 2012-12-06 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: The DMV seminar "Stochastische Approximation und Optimierung zufalliger Systeme" was held at Blaubeuren, 28. 5. -4. 6. 1989. The goal was to give an approach to theory and application of stochas tic approximation in view of optimization problems, especially in engineering systems. These notes are based on the seminar lectures. They consist of three parts: I. Foundations of stochastic approximation (H. Walk); n. Applicational aspects of stochastic approximation (G. PHug); In. Applications to adaptation :ugorithms (L. Ljung). The prerequisites for reading this book are basic knowledge in probability, mathematical statistics, optimization. We would like to thank Prof. M. Barner and Prof. G. Fischer for the or ganization of the seminar. We also thank the participants for their cooperation and our assistants and secretaries for typing the manuscript. November 1991 L. Ljung, G. PHug, H. Walk Table of contents I Foundations of stochastic approximation (H. Walk) §1 Almost sure convergence of stochastic approximation procedures 2 §2 Recursive methods for linear problems 17 §3 Stochastic optimization under stochastic constraints 22 §4 A learning model; recursive density estimation 27 §5 Invariance principles in stochastic approximation 30 §6 On the theory of large deviations 43 References for Part I 45 11 Applicational aspects of stochastic approximation (G. PHug) §7 Markovian stochastic optimization and stochastic approximation procedures 53 §8 Asymptotic distributions 71 §9 Stopping times 79 §1O Applications of stochastic approximation methods 80 References for Part II 90 III Applications to adaptation algorithms (L.
Download or read book Stochastic Approximation and Its Applications written by Han-Fu Chen and published by Springer Science & Business Media. This book was released on 2005-12-30 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: Estimating unknown parameters based on observation data conta- ing information about the parameters is ubiquitous in diverse areas of both theory and application. For example, in system identification the unknown system coefficients are estimated on the basis of input-output data of the control system; in adaptive control systems the adaptive control gain should be defined based on observation data in such a way that the gain asymptotically tends to the optimal one; in blind ch- nel identification the channel coefficients are estimated using the output data obtained at the receiver; in signal processing the optimal weighting matrix is estimated on the basis of observations; in pattern classifi- tion the parameters specifying the partition hyperplane are searched by learning, and more examples may be added to this list. All these parameter estimation problems can be transformed to a root-seeking problem for an unknown function. To see this, let - note the observation at time i. e. , the information available about the unknown parameters at time It can be assumed that the parameter under estimation denoted by is a root of some unknown function This is not a restriction, because, for example, may serve as such a function.
Download or read book Stochastic Approximation written by M. T. Wasan and published by Cambridge University Press. This book was released on 2004-06-03 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: A rigorous mathematical treatment of the technique for studying the properties of an experimental situation.
Download or read book Stochastic Approximation and Recursive Estimation written by Rafail Zalmanovich Hasʹminskii and published by American Mathematical Soc.. This book was released on with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to sequential methods of solving a class of problems to which belongs, for example, the problem of finding a maximum point of a function if each measured value of this function contains a random error. Some basic procedures of stochastic approximation are investigated from a single point of view, namely the theory of Markov processes and martingales. Examples are considered of applications of the theorems to some problems of estimation theory, educational theory and control theory, and also to some problems of information transmission in the presence of inverse feedback.
Download or read book Computational Approaches for Maximum Likelihood Estimation for Nonlinear Mixed Models written by Alan Hughes Hartford and published by . This book was released on 2000 with total page 163 pages. Available in PDF, EPUB and Kindle. Book excerpt: Keywords: Nonlinear regression, Mixed models, Maximum likelihood, Laplace's approximation, Stochastic approximation.
Download or read book Stochastic Approximation and Recursive Estimation written by M. B. Nevel'son and published by American Mathematical Soc.. This book was released on 1976-10-01 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to sequential methods of solving a class of problems to which belongs, for example, the problem of finding a maximum point of a function if each measured value of this function contains a random error. Some basic procedures of stochastic approximation are investigated from a single point of view, namely the theory of Markov processes and martingales. Examples are considered of applications of the theorems to some problems of estimation theory, educational theory and control theory, and also to some problems of information transmission in the presence of inverse feedback.
Download or read book Selected Papers written by Herbert Robbins and published by Springer. This book was released on 2012-12-06 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: Herbert Robbins is widely recognized as one of the most creative and original mathematical statisticians of our time. The purpose of this book is to reprint, on the occasion of his seventieth birthday, some of his most outstanding research. In making selections for reprinting we have tried to keep in mind three potential audiences: (1) the historian who would like to know Robbins' seminal role in stimulating a substantial proportion of current research in mathematical statistics; (2) the novice who would like a readable, conceptually oriented introduction to these subjects; and (3) the expert who would like to have useful reference material in a single collection. In many cases the needs of the first two groups can be met simulta neously. A distinguishing feature of Robbins' research is its daring originality, which literally creates new specialties for subsequent generations of statisticians to explore. Often these seminal papers are also models of exposition serving to introduce the reader, in the simplest possible context, to ideas that are important for contemporary research in the field. An example is the paper of Robbins and Monro which initiated the subject of stochastic approximation. We have also attempted to provide some useful guidance to the literature in various subjects by supplying additional references, particularly to books and survey articles, with some remarks about important developments in these areas.
Download or read book A Stochastic Approximation Algorithm for Maximum Likelihood Estimation in Nonlinear Random Effects Model written by Chi Y. Yuen and published by . This book was released on 1998 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: "We implement a general procedure for incomplete data estimation problems proposed by Gu & Li (1998) and Gu & Kong (1998). The procedure can be used to find the Maximum Likelihood Estimate (MLE) or solve estimating equations in problems such as estimations with censored or truncated regression model, nonlinear structural measurement error model and random effects model. The procedure is based on the general principle of stochastic approximation (Robbins & Monroe 1951) and Markov Chain Monte Carlo method (Metropolis et al. 1953, Hastings 1970). A new stopping criterion is proposed and simulation studies indicate that the algorithm converges consistently to the MLE for the mixed effects logistic regression model." --
Download or read book Handbook of Stochastic Analysis and Applications written by D. Kannan and published by CRC Press. This book was released on 2001-10-23 with total page 800 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to general theories of stochastic processes and modern martingale theory. The volume focuses on consistency, stability and contractivity under geometric invariance in numerical analysis, and discusses problems related to implementation, simulation, variable step size algorithms, and random number generation.
Download or read book Stochastic Approximation written by Vivek S. Borkar and published by Springer. This book was released on 2009-01-01 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Introduction to Stochastic Search and Optimization written by James C. Spall and published by John Wiley & Sons. This book was released on 2005-03-11 with total page 620 pages. Available in PDF, EPUB and Kindle. Book excerpt: * Unique in its survey of the range of topics. * Contains a strong, interdisciplinary format that will appeal to both students and researchers. * Features exercises and web links to software and data sets.
Download or read book Aspects of Gain Constant Selection for Nonlinear Stochastic Approximation by Differential Correction Estimation written by David Randall Hart and published by . This book was released on 1970 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt:
