Robust Methods and Asymptotic Theory in Nonlinear Econometrics by Herman J. Bier

Description: Robust Methods and Asymptotic Theory in Nonlinear Econometrics by Herman J. Bierens 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 nonÂ 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 withÂ out using any instrumental variables at al FORMAT Paperback LANGUAGE English CONDITION Brand New Publisher 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. Notes Springer Book Archives Table of Contents 1 Introduction.- 1.1 Specification and misspecification of the econometric model.- 1.2 The purpose and scope of this study.- 2 Preliminary Mathematics.- 2.1 Random variables, independence, Borel measurable functions and mathematical expectation.- 2.2 Convergence of random variables and distributions.- 2.3 Uniform convergence of random functions.- 2.4 Characteristic functions, stable distributions and a central limit theorem.- 2.5 Unimodal distributions.- 3 Nonlinear Regression Models.- 3.1 Nonlinear least-squares estimation.- 3.2 A class of nonlinear robust M-estimators.- 3.3 Weighted nonlinear robust M-estimation.- 3.4 Miscellaneous notes on robust M-estimation.- 4 Nonlinear Structural Equations.- 4.1 Nonlinear two-stage least squares.- 4.2 Minimum information estimators: introduction.- 4.3 Minimum information estimators: instrumental variable and scaling parameter.- 4.4 Miscellaneous notes on minimum information estimation.- 5 Nonlinear Models with Lagged Dependent Variables.- 5.1 Stochastic stability.- 5.2 Limit theorem for stochastically stable processes.- 5.3 Dynamic nonlinear regression models and implicit structural equations.- 5.4 Remarks on the stochastic stability concept.- 6 Some Applications.- 6.1 Applications of robust M-estimation.- 6.2 An application of minimum information estimation.- References. Promotional Springer Book Archives Long 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 Details ISBN3540108386 Publisher Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Year 1981 ISBN-10 3540108386 ISBN-13 9783540108382 Format Paperback Imprint Springer-Verlag Berlin and Heidelberg GmbH & Co. K Place of Publication Berlin Country of Publication Germany Short Title ROBUST METHODS & ASYMPTOTIC TH Language English Media Book Series Number 192 Publication Date 1981-06-01 DEWEY 330.028 Pages 198 Illustrations IX, 198 p. DOI 10.1007/978-3-642-45529-2 Author Herman J. Bierens Edition Description Softcover reprint of the original 1st ed. 1981 Series Lecture Notes in Economics and Mathematical Systems Audience Professional & Vocational We've got this At The Nile, if you're looking for it, we've got it. With fast shipping, low prices, friendly service and well over a million items - you're bound to find what you want, at a price you'll love! TheNile_Item_ID:96316138;

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