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Author: Russell B. Millar Publisher: John Wiley & Sons ISBN: 1119977711 Category : Mathematics Languages : en Pages : 286
Book Description
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.
Author: Russell B. Millar Publisher: John Wiley & Sons ISBN: 1119977711 Category : Mathematics Languages : en Pages : 286
Book Description
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.
Author: Benedikt M. Pötscher Publisher: Springer Science & Business Media ISBN: 3662034867 Category : Business & Economics Languages : en Pages : 307
Book Description
Many relationships in economics, and also in other fields, are both dynamic and nonlinear. A major advance in econometrics over the last fifteen years has been the development of a theory of estimation and inference for dy namic nonlinear models. This advance was accompanied by improvements in computer technology that facilitate the practical implementation of such estimation methods. In two articles in Econometric Reviews, i.e., Pötscher and Prucha {1991a,b), we provided -an expository discussion of the basic structure of the asymptotic theory of M-estimators in dynamic nonlinear models and a review of the literature up to the beginning of this decade. Among others, the class of M-estimators contains least mean distance estimators (includ ing maximum likelihood estimators) and generalized method of moment estimators. The present book expands and revises the discussion in those articles. It is geared towards the professional econometrician or statistician. Besides reviewing the literature we also presented in the above men tioned articles a number of then new results. One example is a consis tency result for the case where the identifiable uniqueness condition fails.
Author: Michael D. Ward Publisher: Cambridge University Press ISBN: 1107185823 Category : Political Science Languages : en Pages : 327
Book Description
Practical, example-driven introduction to maximum likelihood for the social sciences. Emphasizes computation in R, model selection and interpretation.
Author: Raymond L. Chambers Publisher: CRC Press ISBN: 1584886323 Category : Mathematics Languages : en Pages : 393
Book Description
Sample surveys provide data used by researchers in a large range of disciplines to analyze important relationships using well-established and widely used likelihood methods. The methods used to select samples often result in the sample differing in important ways from the target population and standard application of likelihood methods can lead to biased and inefficient estimates. Maximum Likelihood Estimation for Sample Surveys presents an overview of likelihood methods for the analysis of sample survey data that account for the selection methods used, and includes all necessary background material on likelihood inference. It covers a range of data types, including multilevel data, and is illustrated by many worked examples using tractable and widely used models. It also discusses more advanced topics, such as combining data, non-response, and informative sampling. The book presents and develops a likelihood approach for fitting models to sample survey data. It explores and explains how the approach works in tractable though widely used models for which we can make considerable analytic progress. For less tractable models numerical methods are ultimately needed to compute the score and information functions and to compute the maximum likelihood estimates of the model parameters. For these models, the book shows what has to be done conceptually to develop analyses to the point that numerical methods can be applied. Designed for statisticians who are interested in the general theory of statistics, Maximum Likelihood Estimation for Sample Surveys is also aimed at statisticians focused on fitting models to sample survey data, as well as researchers who study relationships among variables and whose sources of data include surveys.
Author: Yongmiao Hong Publisher: World Scientific ISBN: 9811220204 Category : Business & Economics Languages : en Pages : 523
Book Description
Modern economies are full of uncertainties and risk. Economics studies resource allocations in an uncertain market environment. As a generally applicable quantitative analytic tool for uncertain events, probability and statistics have been playing an important role in economic research. Econometrics is statistical analysis of economic and financial data. In the past four decades or so, economics has witnessed a so-called 'empirical revolution' in its research paradigm, and as the main methodology in empirical studies in economics, econometrics has been playing an important role. It has become an indispensable part of training in modern economics, business and management.This book develops a coherent set of econometric theory, methods and tools for economic models. It is written as a textbook for graduate students in economics, business, management, statistics, applied mathematics, and related fields. It can also be used as a reference book on econometric theory by scholars who may be interested in both theoretical and applied econometrics.
Author: Jan Salomon Cramer Publisher: CUP Archive ISBN: 9780521378574 Category : Business & Economics Languages : en Pages : 232
Book Description
The advent of electronic computing permits the empirical analysis of economic models of far greater subtlety and rigour than before, when many interesting ideas were not followed up because the calculations involved made this impracticable. The estimation and testing of these more intricate models is usually based on the method of Maximum Likelihood, which is a well-established branch of mathematical statistics. Its use in econometrics has led to the development of a number of special techniques; the specific conditions of econometric research moreover demand certain changes in the interpretation of the basic argument. This book is a self-contained introduction to this field. It consists of three parts. The first deals with general features of Maximum Likelihood methods; the second with linear and nonlinear regression; and the third with discrete choice and related micro-economic models. Readers should already be familiar with elementary statistical theory, with applied econometric research papers, or with the literature on the mathematical basis of Maximum Likelihood theory. They can also try their hand at some advanced econometric research of their own.
Author: Jan C. Willems Publisher: Springer Science & Business Media ISBN: 3642750079 Category : Business & Economics Languages : en Pages : 254
Book Description
The problem of obtaining dynamical models directly from an observed time-series occurs in many fields of application. There are a number of possible approaches to this problem. In this volume a number of such points of view are exposed: the statistical time series approach, a theory of guaranted performance, and finally a deterministic approximation approach. This volume is an out-growth of a number of get-togethers sponsered by the Systems and Decision Sciences group of the International Institute of Applied Systems Analysis (IIASA) in Laxenburg, Austria. The hospitality and support of this organization is gratefully acknowledged. Jan Willems Groningen, the Netherlands May 1989 TABLE OF CONTENTS Linear System Identification- A Survey page 1 M. Deistler A Tutorial on Hankel-Norm Approximation 26 K. Glover A Deterministic Approach to Approximate Modelling 49 C. Heij and J. C. Willems Identification - a Theory of Guaranteed Estimates 135 A. B. Kurzhanski Statistical Aspects of Model Selection 215 R. Shibata Index 241 Addresses of Authors 246 LINEAR SYSTEM IDENTIFICATION· A SURVEY M. DEISTLER Abstract In this paper we give an introductory survey on the theory of identification of (in general MIMO) linear systems from (discrete) time series data. The main parts are: Structure theory for linear systems, asymptotic properties of maximum likelihood type estimators, estimation of the dynamic specification by methods based on information criteria and finally, extensions and alternative approaches such as identification of unstable systems and errors-in-variables. Keywords Linear systems, parametrization, maximum likelihood estimation, information criteria, errors-in-variables.
Author: David Pollard Publisher: Springer Science & Business Media ISBN: 1461218802 Category : Mathematics Languages : en Pages : 456
Book Description
Contributed in honour of Lucien Le Cam on the occasion of his 70th birthday, the papers reflect the immense influence that his work has had on modern statistics. They include discussions of his seminal ideas, historical perspectives, and contributions to current research - spanning two centuries with a new translation of a paper of Daniel Bernoulli. The volume begins with a paper by Aalen, which describes Le Cams role in the founding of the martingale analysis of point processes, and ends with one by Yu, exploring the position of just one of Le Cams ideas in modern semiparametric theory. The other 27 papers touch on areas such as local asymptotic normality, contiguity, efficiency, admissibility, minimaxity, empirical process theory, and biological medical, and meteorological applications - where Le Cams insights have laid the foundations for new theories.
Author: Scott R. Eliason Publisher: SAGE ISBN: 9780803941076 Category : Mathematics Languages : en Pages : 100
Book Description
This is a short introduction to Maximum Likelihood (ML) Estimation. It provides a general modeling framework that utilizes the tools of ML methods to outline a flexible modeling strategy that accommodates cases from the simplest linear models (such as the normal error regression model) to the most complex nonlinear models linking endogenous and exogenous variables with non-normal distributions. Using examples to illustrate the techniques of finding ML estimators and estimates, the author discusses what properties are desirable in an estimator, basic techniques for finding maximum likelihood solutions, the general form of the covariance matrix for ML estimates, the sampling distribution of ML estimators; the use of ML in the normal as well as other distributions, and some useful illustrations of likelihoods.
Author: M. Ishaq Bhatti Publisher: Routledge ISBN: 135194195X Category : Business & Economics Languages : en Pages : 286
Book Description
In recent years econometricians have examined the problems of diagnostic testing, specification testing, semiparametric estimation and model selection. In addition researchers have considered whether to use model testing and model selection procedures to decide the models that best fit a particular dataset. This book explores both issues with application to various regression models, including the arbitrage pricing theory models. It is ideal as a reference for statistical sciences postgraduate students, academic researchers and policy makers in understanding the current status of model building and testing techniques.
Author: Russell B. Millar
Author: Russell B. Millar
Author: Benedikt M. Pötscher
Author: Michael D. Ward
Author: Raymond L. Chambers
Author: Yongmiao Hong
Author: Jan Salomon Cramer
Author: Jan C. Willems
Author: David Pollard
Author: Scott R. Eliason
Author: M. Ishaq Bhatti