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Author: H. J. Bierens
Publisher: Springer Science & Business Media
ISBN: 3642455298
Category : Mathematics
Languages : en
Pages : 211
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Book Description
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: H. J. Bierens
Publisher: Springer Science & Business Media
ISBN: 3642455298
Category : Mathematics
Languages : en
Pages : 211
Get Book Here
Book Description
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: William A. Barnett
Publisher: Cambridge University Press
ISBN: 9780521594240
Category : Business & Economics
Languages : en
Pages : 248
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Book Description
This book presents some of the more recent developments in nonlinear time series, including Bayesian analysis and cointegration tests.
Author: W.J.J. Rey
Publisher: Springer Science & Business Media
ISBN: 364269389X
Category : Mathematics
Languages : en
Pages : 247
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Book Description
Author: Benedikt M. Pötscher
Publisher: Springer Science & Business Media
ISBN: 3662034867
Category : Business & Economics
Languages : en
Pages : 307
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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: Tadeusz Calinski
Publisher: Springer Science & Business Media
ISBN: 9401110042
Category : Mathematics
Languages : en
Pages : 309
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Book Description
The International Conference on Linear Statistical Inference LINSTAT'93 was held in Poznan, Poland, from May 31 to June 4, 1993. The purpose of the confer ence was to enable scientists, from various countries, engaged in the diverse areas of statistical sciences and practice to meet together and exchange views and re sults related to the current research on linear statistical inference in its broadest sense. Thus, the conference programme included sessions on estimation, prediction and testing in linear models, on robustness of some relevant statistical methods, on estimation of variance components appearing in linear models, on certain gen eralizations to nonlinear models, on design and analysis of experiments, including optimality and comparison of linear experiments, and on some other topics related to linear statistical inference. Within the various sessions 22 invited papers and 37 contributed papers were presented, 12 of them as posters. The conference gathered 94 participants from eighteen countries of Europe, North America and Asia. There were 53 participants from abroad and 41 from Poland. The conference was the second of this type, devoted to linear statistical inference. The first was held in Poznan in June, 4-8, 1984. Both belong to the series of confer ences on mathematical statistics and probability theory organized under the auspices of the Committee of Mathematics of the Polish Academy of Sciences, due to the ini tiative and efforts of its Mathematical Statistics Section. In the years 1973-1993 there were held in Poland nineteen such conferences, some of them international.
Author: Herman J. Bierens
Publisher: Cambridge University Press
ISBN: 9780521542241
Category : Business & Economics
Languages : en
Pages : 356
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Book Description
This book is intended for use in a rigorous introductory PhD level course in econometrics.
Author: P. C. B. Phillips
Publisher: Cambridge University Press
ISBN: 9780521807234
Category : Business & Economics
Languages : en
Pages : 390
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Book Description
The essays in this book explore important theoretical and applied advances in econometrics.
Author: George G. Judge
Publisher: John Wiley & Sons
ISBN: 047189530X
Category : Business & Economics
Languages : en
Pages : 1062
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Book Description
This broadly based graduate-level textbook covers the major models and statistical tools currently used in the practice of econometrics. It examines the classical, the decision theory, and the Bayesian approaches, and contains material on single equation and simultaneous equation econometric models. Includes an extensive reference list for each topic.
Author: A. Ronald Gallant
Publisher: John Wiley & Sons
ISBN: 047031737X
Category : Mathematics
Languages : en
Pages : 633
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Book Description
A comprehensive text and reference bringing together advances in the theory of probability and statistics and relating them to applications. The three major categories of statistical models that relate dependent variables to explanatory variables are covered: univariate regression models, multivariate regression models, and simultaneous equations models. Methods are illustrated with worked examples, complete with figures that display code and output.
Author: Fritz K. Brunner
Publisher: Springer
ISBN: 3540469613
Category : Science
Languages : en
Pages : 252
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Book Description
This selection of papers emphasizes the advances in the field and covers a wide range of topics in geophysics, geodynamics, and oceanography to which modern geodesy is contributing.
