Small Sample Properties of Estimators of Non-linear Models of Covariance Structure PDF Download

Author: Todd E. Clark (Economiste)
Publisher:
ISBN:
Category :
Languages : en
Pages : 104

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Author: Todd E. Clark
Publisher:
ISBN:
Category : Analysis of covariance
Languages : en
Pages : 104

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Book Description

Author: Erik Grafarend
Publisher: Springer Science & Business Media
ISBN: 3642222412
Category : Science
Languages : en
Pages : 1026

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Book Description
Here we present a nearly complete treatment of the Grand Universe of linear and weakly nonlinear regression models within the first 8 chapters. Our point of view is both an algebraic view as well as a stochastic one. For example, there is an equivalent lemma between a best, linear uniformly unbiased estimation (BLUUE) in a Gauss-Markov model and a least squares solution (LESS) in a system of linear equations. While BLUUE is a stochastic regression model, LESS is an algebraic solution. In the first six chapters we concentrate on underdetermined and overdeterimined linear systems as well as systems with a datum defect. We review estimators/algebraic solutions of type MINOLESS, BLIMBE, BLUMBE, BLUUE, BIQUE, BLE, BIQUE and Total Least Squares. The highlight is the simultaneous determination of the first moment and the second central moment of a probability distribution in an inhomogeneous multilinear estimation by the so called E-D correspondence as well as its Bayes design. In addition, we discuss continuous networks versus discrete networks, use of Grassmann-Pluecker coordinates, criterion matrices of type Taylor-Karman as well as FUZZY sets. Chapter seven is a speciality in the treatment of an overdetermined system of nonlinear equations on curved manifolds. The von Mises-Fisher distribution is characteristic for circular or (hyper) spherical data. Our last chapter eight is devoted to probabilistic regression, the special Gauss-Markov model with random effects leading to estimators of type BLIP and VIP including Bayesian estimation. A great part of the work is presented in four Appendices. Appendix A is a treatment, of tensor algebra, namely linear algebra, matrix algebra and multilinear algebra. Appendix B is devoted to sampling distributions and their use in terms of confidence intervals and confidence regions. Appendix C reviews the elementary notions of statistics, namely random events and stochastic processes. Appendix D introduces the basics of Groebner basis algebra, its careful definition, the Buchberger Algorithm, especially the C. F. Gauss combinatorial algorithm.

Author: Robin C. Sickles
Publisher: Springer Science & Business Media
ISBN: 1489980083
Category : Business & Economics
Languages : en
Pages : 417

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Book Description
From the Introduction: This volume is dedicated to the remarkable career of Professor Peter Schmidt and the role he has played in mentoring us, his PhD students. Peter’s accomplishments are legendary among his students and the profession. Each of the papers in this Festschrift is a research work executed by a former PhD student of Peter’s, from his days at the University of North Carolina at Chapel Hill to his time at Michigan State University. Most of the papers were presented at The Conference in Honor of Peter Schmidt, June 30 - July 2, 2011. The conference was largely attended by his former students and one current student, who traveled from as far as Europe and Asia to honor Peter. This was a conference to celebrate Peter’s contribution to our contributions. By “our contributions” we mean the research papers that make up this Festschrift and the countless other publications by his students represented and not represented in this volume. Peter’s students may have their families to thank for much that is positive in their lives. However, if we think about it, our professional lives would not be the same without the lessons and the approaches to decision making that we learned from Peter. We spent our days together at Peter’s conference and the months since reminded of these aspects of our personalities and life goals that were enhanced, fostered, and nurtured by the very singular experiences we have had as Peter’s students. We recognized in 2011 that it was unlikely we would all be together again to celebrate such a wonderful moment in ours and Peter’s lives and pledged then to take full advantage of it. We did then, and we are now in the form of this volume.

Author: Joseph G. Altonji
Publisher:
ISBN:
Category : Analysis of covariance
Languages : en
Pages : 64

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Book Description
We examine the small sample properties of the GMM estimator for models of covariance structures, where the technique is often referred to as the optimal minimum distance (OMD) estimator. We present a variety of Monte Carlo experiments based on simulated data and on the data used by Abowd and Card (1987, 1990) in an examination of the covariance structure of hours and earnings changes. Our main finding is that OMD is seriously biased in small samples for many distributions and in relatively large samples for poorly behaved distributions. The bias is almost always downward in absolute value. It arises because sampling errors in the second moments are correlated with sampling errors in the weighting matrix used by OMD. Furthermore, OMD usually has a larger root mean square error and median absolute error than equally weighted minimum distance (EWMD). We also propose and investigate an alternative estimator, which we call independently weighted optimal minimum distance (IWOMD). IWOMD is a split sample estimator using separate groups of observations to estimate the moments and the weights. IWOMD has identical large sample properties to the OMD estimator but is unbiased regardless of sample size. However, the Monte Carlo evidence indicates that IWOMD is usually dominated by EWMD.

Author: Minbo Kim
Publisher:
ISBN:
Category : Econometrics
Languages : en
Pages : 396

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Book Description

Author: Alastair R. Hall
Publisher: Oxford University Press
ISBN: 0198775210
Category : Business & Economics
Languages : en
Pages : 413

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Book Description
Generalized Method of Moments (GMM) has become one of the main statistical tools for the analysis of economic and financial data. This book is the first to provide an intuitive introduction to the method combined with a unified treatment of GMM statistical theory and a survey of recentimportant developments in the field. Providing a comprehensive treatment of GMM estimation and inference, it is designed as a resource for both the theory and practice of GMM: it discusses and proves formally all the main statistical results, and illustrates all inference techniques using empiricalexamples in macroeconomics and finance.Building from the instrumental variables estimator in static linear models, it presents the asymptotic statistical theory of GMM in nonlinear dynamic models. Within this framework it covers classical results on estimation and inference techniques, such as the overidentifying restrictions test andtests of structural stability, and reviews the finite sample performance of these inference methods. And it discusses in detail recent developments on covariance matrix estimation, the impact of model misspecification, moment selection, the use of the bootstrap, and weak instrumentasymptotics.

Author: Laszlo Matyas
Publisher: Cambridge University Press
ISBN: 9780521669672
Category : Business & Economics
Languages : en
Pages : 332

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Book Description
The generalized method of moments (GMM) estimation has emerged as providing a ready to use, flexible tool of application to a large number of econometric and economic models by relying on mild, plausible assumptions. The principal objective of this volume is to offer a complete presentation of the theory of GMM estimation as well as insights into the use of these methods in empirical studies. It is also designed to serve as a unified framework for teaching estimation theory in econometrics. Contributors to the volume include well-known authorities in the field based in North America, the UK/Europe, and Australia. The work is likely to become a standard reference for graduate students and professionals in economics, statistics, financial modeling, and applied mathematics.

Author: William H. Greene
Publisher:
ISBN:
Category :
Languages : en
Pages : 23

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Book Description
The nonlinear fixed effects models in econometrics has often been avoided for two reasons one practical, one methodological. The practical obstacle relates to the difficulty of estimating nonlinear models with possibly thousands of coefficients. In fact, in a large number of models of interest to practitioners, estimation of the fixed effects model is feasible even in panels with very large numbers of groups. The more difficult, methodological question centers on the incidental parameters problem that raises questions about the statistical properties of the estimator. There is very little empirical evidence on the behavior of the fixed effects estimator. In this note, we use Monte Carlo methods to examine the small sample bias in the binary probit and logit models, the ordered probit model, the tobit model, the Poisson regression model for count data and the exponential regression model for a nonnegative random variable. We find three results of note: A widely accepted result that suggests that the probit estimator is actually relatively well behaved appears to be incorrect. Perhaps to some surprise, the tobit model, unlike the others, appears largely to be unaffected by the incidental parameters problem, save for a surprising result related to the disturbance variance estimator. Third, as apparently unexamined previously, the estimated asymptotic estimators for fixed effects estimators appear uniformly to be downward biased.

Author: Alvin C. Rencher
Publisher: John Wiley & Sons
ISBN: 0470192607
Category : Mathematics
Languages : en
Pages : 690

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Book Description
The essential introduction to the theory and application of linear models—now in a valuable new edition Since most advanced statistical tools are generalizations of the linear model, it is neces-sary to first master the linear model in order to move forward to more advanced concepts. The linear model remains the main tool of the applied statistician and is central to the training of any statistician regardless of whether the focus is applied or theoretical. This completely revised and updated new edition successfully develops the basic theory of linear models for regression, analysis of variance, analysis of covariance, and linear mixed models. Recent advances in the methodology related to linear mixed models, generalized linear models, and the Bayesian linear model are also addressed. Linear Models in Statistics, Second Edition includes full coverage of advanced topics, such as mixed and generalized linear models, Bayesian linear models, two-way models with empty cells, geometry of least squares, vector-matrix calculus, simultaneous inference, and logistic and nonlinear regression. Algebraic, geometrical, frequentist, and Bayesian approaches to both the inference of linear models and the analysis of variance are also illustrated. Through the expansion of relevant material and the inclusion of the latest technological developments in the field, this book provides readers with the theoretical foundation to correctly interpret computer software output as well as effectively use, customize, and understand linear models. This modern Second Edition features: New chapters on Bayesian linear models as well as random and mixed linear models Expanded discussion of two-way models with empty cells Additional sections on the geometry of least squares Updated coverage of simultaneous inference The book is complemented with easy-to-read proofs, real data sets, and an extensive bibliography. A thorough review of the requisite matrix algebra has been addedfor transitional purposes, and numerous theoretical and applied problems have been incorporated with selected answers provided at the end of the book. A related Web site includes additional data sets and SAS® code for all numerical examples. Linear Model in Statistics, Second Edition is a must-have book for courses in statistics, biostatistics, and mathematics at the upper-undergraduate and graduate levels. It is also an invaluable reference for researchers who need to gain a better understanding of regression and analysis of variance.