On the Asymptotic Properties of Parameter Estimates in a Regression Model with Non-Normally Distributed Errors PDF Download

Author: John L. Maryak
Publisher:
ISBN:
Category :
Languages : en
Pages : 5

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Book Description
The usual assumption of normality for the error terms of a regression model is often untenable. When this assumption is dropped, it may be difficult to characterize parameter estimates for the model. For example, it is stated that if the regression errors are non-normal, one is not even sure of their (e.g., the generalized least squares parameter estimates') asymptotic properties. A partial answer presents an asymptotic distribution theory for Kalman filter estimates for cases where the random terms of the state space model are not necessarily Gaussian. Certain of these asymptotic distribution results are also discussed in the context of model validation (diagnostic checking). Keywords: Random coefficient regression, State-space model, Non-Gaussian, Kalman filters, Reprints. (JHD).

Author: Werner Stahel
Publisher: Springer Science & Business Media
ISBN: 1461244447
Category : Mathematics
Languages : en
Pages : 384

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This IMA Volume in Mathematics and its Applications DIRECTIONS IN ROBUST STATISTICS AND DIAGNOSTICS is based on the proceedings of the first four weeks of the six week IMA 1989 summer program "Robustness, Diagnostics, Computing and Graphics in Statistics". An important objective of the organizers was to draw a broad set of statisticians working in robustness or diagnostics into collaboration on the challenging problems in these areas, particularly on the interface between them. We thank the organizers of the robustness and diagnostics program Noel Cressie, Thomas P. Hettmansperger, Peter J. Huber, R. Douglas Martin, and especially Werner Stahel and Sanford Weisberg who edited the proceedings. A vner Friedman Willard Miller, Jr. PREFACE Central themes of all statistics are estimation, prediction, and making decisions under uncertainty. A standard approach to these goals is through parametric mod elling. Parametric models can give a problem sufficient structure to allow standard, well understood paradigms to be applied to make the required inferences. If, how ever, the parametric model is not completely correct, then the standard inferential methods may not give reasonable answers. In the last quarter century, particularly with the advent of readily available computing, more attention has been paid to the problem of inference when the parametric model used is not correctly specified.

Author: H. J. Bierens
Publisher: Springer Science & Business Media
ISBN: 3642455298
Category : Mathematics
Languages : en
Pages : 211

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This Lecture Note deals with asymptotic properties, i.e. weak and strong consistency and asymptotic normality, of parameter estimators of nonlinear regression models and nonlinear structural equations under various assumptions on the distribution of the data. The estimation methods involved are nonlinear least squares estimation (NLLSE), nonlinear robust M-estimation (NLRME) and non linear weighted robust M-estimation (NLWRME) for the regression case and nonlinear two-stage least squares estimation (NL2SLSE) and a new method called minimum information estimation (MIE) for the case of structural equations. The asymptotic properties of the NLLSE and the two robust M-estimation methods are derived from further elaborations of results of Jennrich. Special attention is payed to the comparison of the asymptotic efficiency of NLLSE and NLRME. It is shown that if the tails of the error distribution are fatter than those of the normal distribution NLRME is more efficient than NLLSE. The NLWRME method is appropriate if the distributions of both the errors and the regressors have fat tails. This study also improves and extends the NL2SLSE theory of Amemiya. The method involved is a variant of the instrumental variables method, requiring at least as many instrumental variables as parameters to be estimated. The new MIE method requires less instrumental variables. Asymptotic normality can be derived by employing only one instrumental variable and consistency can even be proved with out using any instrumental variables at all.

Author: Advisory Committee on Technology and Society
Publisher: National Academies Press
ISBN: 9780309037860
Category : Social Science
Languages : en
Pages : 1298

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Cities and Their Vital Systems asks basic questions about the longevity, utility, and nature of urban infrastructures; analyzes how they grow, interact, and change; and asks how, when, and at what cost they should be replaced. Among the topics discussed are problems arising from increasing air travel and airport congestion; the adequacy of water supplies and waste treatment; the impact of new technologies on construction; urban real estate values; and the field of "telematics," the combination of computers and telecommunications that makes money machines and national newspapers possible.

Author:
Publisher:
ISBN:
Category : Science
Languages : en
Pages : 534

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Author: Jiming Jiang
Publisher: CRC Press
ISBN: 1351645595
Category : Mathematics
Languages : en
Pages : 235

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Book Description
Large sample techniques are fundamental to all fields of statistics. Mixed effects models, including linear mixed models, generalized linear mixed models, non-linear mixed effects models, and non-parametric mixed effects models are complex models, yet, these models are extensively used in practice. This monograph provides a comprehensive account of asymptotic analysis of mixed effects models. The monograph is suitable for researchers and graduate students who wish to learn about asymptotic tools and research problems in mixed effects models. It may also be used as a reference book for a graduate-level course on mixed effects models, or asymptotic analysis.

Author: Sharif Hossain
Publisher: Cambridge Scholars Publishing
ISBN: 1527563413
Category : Business & Economics
Languages : en
Pages : 741

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Book Description
For the last four decades, the uses of econometric tools and techniques, irrespective of discipline, have been increasing rapidly for solving problems, appropriate decision-making and policy formulation. Generally, it is accepted that the study of modern business and economics is incomplete without a proper knowledge of econometric tools and techniques. In view of the increasing complexity and variety of problems in business and economics, students and researchers may not be able to cope and hence may remain unfamiliar with many aspects of business and economic problems. Thus, this book was written to explore basic and advanced studies of econometrics for undergraduate and graduate students of business and economics, as well as for researchers already engaged in these fields who require an introduction to econometric methods and their application for solving of real-life problems. The book offers a balanced presentation of fundamental and advanced levels of econometric concepts and methods, along with practical examples of their effective application in real-life problems.

Author: R. Carter Hill
Publisher: John Wiley & Sons
ISBN: 1118452275
Category : Business & Economics
Languages : en
Pages : 1808

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Book Description
Principles of Econometrics, Fifth Edition, is an introductory book for undergraduate students in economics and finance, as well as first-year graduate students in a variety of fields that include economics, finance, accounting, marketing, public policy, sociology, law, and political science. Students will gain a working knowledge of basic econometrics so they can apply modeling, estimation, inference, and forecasting techniques when working with real-world economic problems. Readers will also gain an understanding of econometrics that allows them to critically evaluate the results of others’ economic research and modeling, and that will serve as a foundation for further study of the field. This new edition of the highly-regarded econometrics text includes major revisions that both reorganize the content and present students with plentiful opportunities to practice what they have read in the form of chapter-end exercises.

Author: Otto J.W.F. Kardaun
Publisher: Springer Science & Business Media
ISBN: 3540292888
Category : Science
Languages : en
Pages : 396

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Book Description
Classical Methods of Statistics is a guidebook combining theory and practical methods. It is especially conceived for graduate students and scientists who are interested in the applications of statistical methods to plasma physics. Thus it provides also concise information on experimental aspects of fusion-oriented plasma physics. In view of the first three basic chapters it can be fruitfully used by students majoring in probability theory and statistics. The first part deals with the mathematical foundation and framework of the subject. Some attention is given to the historical background. Exercises are added to help readers understand the underlying concepts. In the second part, two major case studies are presented which exemplify the areas of discriminant analysis and multivariate profile analysis, respectively. To introduce these case studies, an outline is provided of the context of magnetic plasma fusion research. In the third part an overview is given of statistical software; separate attention is devoted to SAS and S-PLUS. The final chapter presents several datasets and gives a description of their physical setting. Most of these datasets were assembled at the ASDEX Upgrade Tokamak. All of them are accompanied by exercises in form of guided (minor) case studies. The book concludes with translations of key concepts into several languages.

Author:
Publisher:
ISBN:
Category : Weights and measures
Languages : en
Pages : 574

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