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Author: Vance Martin
Publisher: Cambridge University Press
ISBN: 0521139813
Category : Business & Economics
Languages : en
Pages : 925
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Book Description
"Maximum likelihood estimation is a general method for estimating the parameters of econometric models from observed data. The principle of maximum likelihood plays a central role in the exposition of this book, since a number of estimators used in econometrics can be derived within this framework. Examples include ordinary least squares, generalized least squares and full-information maximum likelihood. In deriving the maximum likelihood estimator, a key concept is the joint probability density function (pdf) of the observed random variables, yt. Maximum likelihood estimation requires that the following conditions are satisfied. (1) The form of the joint pdf of yt is known. (2) The specification of the moments of the joint pdf are known. (3) The joint pdf can be evaluated for all values of the parameters, 9. Parts ONE and TWO of this book deal with models in which all these conditions are satisfied. Part THREE investigates models in which these conditions are not satisfied and considers four important cases. First, if the distribution of yt is misspecified, resulting in both conditions 1 and 2 being violated, estimation is by quasi-maximum likelihood (Chapter 9). Second, if condition 1 is not satisfied, a generalized method of moments estimator (Chapter 10) is required. Third, if condition 2 is not satisfied, estimation relies on nonparametric methods (Chapter 11). Fourth, if condition 3 is violated, simulation-based estimation methods are used (Chapter 12). 1.2 Motivating Examples To highlight the role of probability distributions in maximum likelihood estimation, this section emphasizes the link between observed sample data and 4 The Maximum Likelihood Principle the probability distribution from which they are drawn"-- publisher.
Author: Vance Martin
Publisher: Cambridge University Press
ISBN: 0521139813
Category : Business & Economics
Languages : en
Pages : 925
Get Book Here
Book Description
"Maximum likelihood estimation is a general method for estimating the parameters of econometric models from observed data. The principle of maximum likelihood plays a central role in the exposition of this book, since a number of estimators used in econometrics can be derived within this framework. Examples include ordinary least squares, generalized least squares and full-information maximum likelihood. In deriving the maximum likelihood estimator, a key concept is the joint probability density function (pdf) of the observed random variables, yt. Maximum likelihood estimation requires that the following conditions are satisfied. (1) The form of the joint pdf of yt is known. (2) The specification of the moments of the joint pdf are known. (3) The joint pdf can be evaluated for all values of the parameters, 9. Parts ONE and TWO of this book deal with models in which all these conditions are satisfied. Part THREE investigates models in which these conditions are not satisfied and considers four important cases. First, if the distribution of yt is misspecified, resulting in both conditions 1 and 2 being violated, estimation is by quasi-maximum likelihood (Chapter 9). Second, if condition 1 is not satisfied, a generalized method of moments estimator (Chapter 10) is required. Third, if condition 2 is not satisfied, estimation relies on nonparametric methods (Chapter 11). Fourth, if condition 3 is violated, simulation-based estimation methods are used (Chapter 12). 1.2 Motivating Examples To highlight the role of probability distributions in maximum likelihood estimation, this section emphasizes the link between observed sample data and 4 The Maximum Likelihood Principle the probability distribution from which they are drawn"-- publisher.
Author: Halbert White
Publisher: Cambridge University Press
ISBN: 9780521574464
Category : Business & Economics
Languages : en
Pages : 396
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Book Description
This book examines the consequences of misspecifications for the interpretation of likelihood-based methods of statistical estimation and interference. The analysis concludes with an examination of methods by which the possibility of misspecification can be empirically investigated.
Author: Jan Kmenta
Publisher: Academic Press
ISBN: 1483267342
Category : Business & Economics
Languages : en
Pages : 425
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Book Description
Evaluation of Econometric Models presents approaches to assessing and enhancing the progress of applied economic research. This book discusses the problems and issues in evaluating econometric models, use of exploratory methods in economic analysis, and model construction and evaluation when theoretical knowledge is scarce. The data analysis by partial least squares, prediction analysis of economic models, and aggregation and disaggregation of nonlinear equations are also elaborated. This text likewise covers the comparison of econometric models by optimal control techniques, role of time series analysis in econometric model evaluation, and hypothesis testing in spectral regression. Other topics include the relevance of laboratory experiments to testing resource allocation theory and token economy and animal models for the experimental analysis of economic behavior. This publication is intended for students and researchers interested in evaluating econometric models.
Author: T. Fomby
Publisher: Elsevier
ISBN: 9780762310753
Category : Business & Economics
Languages : en
Pages : 280
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Book Description
Comparative study of pure and pretest estimators for a possibly misspecified two-way error component model / Badi H. Baltagi, Georges Bresson, Alain Pirotte -- Estimation, inference, and specification testing for possibly misspecified quantile regression / Tae-Hwan Kim, Halbert White -- Quasimaximum likelihood estimation with bounded symmetric errors / Douglas Miller, James Eales, Paul Preckel -- Consistent quasi-maximum likelihood estimation with limited information / Douglas Miller, Sang-Hak Lee -- An examination of the sign and volatility switching arch models under alternative distributional assumptions / Mohamed F. Omran, Florin Avram -- estimating a linear exponential density when the weighting matrix and mean parameter vector are functionally related / Chor-yiu Sin -- Testing in GMM models without truncation / Timothy J. Vogelsang -- Bayesian analysis of misspecified models with fixed effects / Tiemen Woutersen -- Tests of common deterministic trend slopes applied to quarterly global temperature data / Thomas B. Fomby, Timothy J. Vogelsang -- The sandwich estimate of variance / James W. Hardin -- Test statistics and critical values in selectivity models / R. Carter Hill, Lee C. Adkins, Keith A. Bender -- Introduction / Thomas B Fomby, R. Carter Hill.
Author: Yongmiao Hong
Publisher: World Scientific
ISBN: 9811220204
Category : Business & Economics
Languages : en
Pages : 523
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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: Mark J. van der Laan
Publisher: Springer Science & Business Media
ISBN: 1441997822
Category : Mathematics
Languages : en
Pages : 628
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Book Description
The statistics profession is at a unique point in history. The need for valid statistical tools is greater than ever; data sets are massive, often measuring hundreds of thousands of measurements for a single subject. The field is ready to move towards clear objective benchmarks under which tools can be evaluated. Targeted learning allows (1) the full generalization and utilization of cross-validation as an estimator selection tool so that the subjective choices made by humans are now made by the machine, and (2) targeting the fitting of the probability distribution of the data toward the target parameter representing the scientific question of interest. This book is aimed at both statisticians and applied researchers interested in causal inference and general effect estimation for observational and experimental data. Part I is an accessible introduction to super learning and the targeted maximum likelihood estimator, including related concepts necessary to understand and apply these methods. Parts II-IX handle complex data structures and topics applied researchers will immediately recognize from their own research, including time-to-event outcomes, direct and indirect effects, positivity violations, case-control studies, censored data, longitudinal data, and genomic studies.
Author: Jan C. Willems
Publisher: Springer Science & Business Media
ISBN: 3642750079
Category : Business & Economics
Languages : en
Pages : 254
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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: Russell B. Millar
Publisher: John Wiley & Sons
ISBN: 1119977711
Category : Mathematics
Languages : en
Pages : 286
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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: Theo K. Dijkstra
Publisher: Springer Science & Business Media
ISBN: 3642954618
Category : Business & Economics
Languages : en
Pages : 139
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Book Description
Author: Daniel Straumann
Publisher: Springer Science & Business Media
ISBN: 3540269789
Category : Business & Economics
Languages : en
Pages : 239
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Book Description
In his seminal 1982 paper, Robert F. Engle described a time series model with a time-varying volatility. Engle showed that this model, which he called ARCH (autoregressive conditionally heteroscedastic), is well-suited for the description of economic and financial price. Nowadays ARCH has been replaced by more general and more sophisticated models, such as GARCH (generalized autoregressive heteroscedastic). This monograph concentrates on mathematical statistical problems associated with fitting conditionally heteroscedastic time series models to data. This includes the classical statistical issues of consistency and limiting distribution of estimators. Particular attention is addressed to (quasi) maximum likelihood estimation and misspecified models, along to phenomena due to heavy-tailed innovations. The used methods are based on techniques applied to the analysis of stochastic recurrence equations. Proofs and arguments are given wherever possible in full mathematical rigour. Moreover, the theory is illustrated by examples and simulation studies.
