Asymptotic Theory Of Nonlinear Regression

Author : A.A. Ivanov
Publisher : Springer Science & Business Media
ISBN 13 : 9401588775
Total Pages : 333 pages
Book Rating : 4.75/5 ( download)

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Download or read book Asymptotic Theory of Nonlinear Regression written by A.A. Ivanov and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: Let us assume that an observation Xi is a random variable (r.v.) with values in 1 1 (1R1 , 8 ) and distribution Pi (1R1 is the real line, and 8 is the cr-algebra of its Borel subsets). Let us also assume that the unknown distribution Pi belongs to a 1 certain parametric family {Pi() , () E e}. We call the triple £i = {1R1 , 8 , Pi(), () E e} a statistical experiment generated by the observation Xi. n We shall say that a statistical experiment £n = {lRn, 8 , P; ,() E e} is the product of the statistical experiments £i, i = 1, ... ,n if PO' = P () X ... X P () (IRn 1 n n is the n-dimensional Euclidean space, and 8 is the cr-algebra of its Borel subsets). In this manner the experiment £n is generated by n independent observations X = (X1, ... ,Xn). In this book we study the statistical experiments £n generated by observations of the form j = 1, ... ,n. (0.1) Xj = g(j, (}) + cj, c c In (0.1) g(j, (}) is a non-random function defined on e , where e is the closure in IRq of the open set e ~ IRq, and C j are independent r. v .-s with common distribution function (dJ.) P not depending on ().

Author : A. A. Ivanov
Publisher :
ISBN 13 : 9789401588782
Total Pages : 342 pages
Book Rating : 4.83/5 ( download)

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Download or read book Asymptotic Theory of Nonlinear Regression written by A. A. Ivanov and published by . This book was released on 2014-01-15 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : H. J. Bierens
Publisher : Springer Science & Business Media
ISBN 13 : 3642455298
Total Pages : 211 pages
Book Rating : 4.92/5 ( download)

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Download or read book Robust Methods and Asymptotic Theory in Nonlinear Econometrics written by H. J. Bierens and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 211 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
ISBN 13 : 9783642455308
Total Pages : 198 pages
Book Rating : 4.01/5 ( download)

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Download or read book Robust Methods and Asymptotic Theory in Nonlinear Econometrics written by H. J. Bierens and published by Springer. This book was released on 2012-03-02 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : George A. F. Seber
Publisher : John Wiley & Sons
ISBN 13 : 0471725307
Total Pages : 768 pages
Book Rating : 4.05/5 ( download)

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Download or read book Nonlinear Regression written by George A. F. Seber and published by John Wiley & Sons. This book was released on 2005-02-25 with total page 768 pages. Available in PDF, EPUB and Kindle. Book excerpt: WILEY-INTERSCIENCE PAPERBACK SERIES The Wiley-Interscience Paperback Series consists of selected books that have been made more accessible to consumers in an effort to increase global appeal and general circulation. With these new unabridged softcover volumes, Wiley hopes to extend the lives of these works by making them available to future generations of statisticians, mathematicians, and scientists. From the Reviews of Nonlinear Regression "A very good book and an important one in that it is likely to become a standard reference for all interested in nonlinear regression; and I would imagine that any statistician concerned with nonlinear regression would want a copy on his shelves." –The Statistician "Nonlinear Regression also includes a reference list of over 700 entries. The compilation of this material and cross-referencing of it is one of the most valuable aspects of the book. Nonlinear Regression can provide the researcher unfamiliar with a particular specialty area of nonlinear regression an introduction to that area of nonlinear regression and access to the appropriate references . . . Nonlinear Regression provides by far the broadest discussion of nonlinear regression models currently available and will be a valuable addition to the library of anyone interested in understanding and using such models including the statistical researcher." –Mathematical Reviews

Author : Herman J. Bierens
Publisher : Springer
ISBN 13 :
Total Pages : 214 pages
Book Rating : 4.16/5 ( download)

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Download or read book Robust Methods and Asymptotic Theory in Nonlinear Econometrics written by Herman J. Bierens and published by Springer. This book was released on 1981 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Benedikt M. Pötscher
Publisher : Springer Science & Business Media
ISBN 13 : 3662034867
Total Pages : 307 pages
Book Rating : 4.66/5 ( download)

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Download or read book Dynamic Nonlinear Econometric Models written by Benedikt M. Pötscher and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : José Francisco Burguete
Publisher :
ISBN 13 :
Total Pages : 160 pages
Book Rating : 4.71/5 ( download)

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Download or read book Asymptotic Theory of Instrumental Variables in Nonlinear Regression written by José Francisco Burguete and published by . This book was released on 1980 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Chien-Fu WU
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.22/5 ( download)

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Download or read book ASYMPTOTIC THEORY OF NONLINEAR LEAST SQUARES ESTIMATION written by Chien-Fu WU and published by . This book was released on 1979 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : A. Ronald Gallant
Publisher : John Wiley & Sons
ISBN 13 :
Total Pages : 632 pages
Book Rating : 4.16/5 ( download)

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Download or read book Nonlinear Statistical Models written by A. Ronald Gallant and published by John Wiley & Sons. This book was released on 1987-02-04 with total page 632 pages. Available in PDF, EPUB and Kindle. Book excerpt: Univariate nonlinear regression; Univariate nonlinear regression: special situations; A unified asymptotic theory of nonlinear models with regression structure; Univariate nonlinear regression: asymptotic theory; Multivariate nonlinear regression; Nonlinear simultaneus equations models; A unified asymptotic theory for dynamic nonlinear models.