Robust Methods and Asymptotic Theory in Nonlinear Econometrics

Bierens H. J.

ISBN 10: 3540108386 / ISBN 13: 9783540108382

Published by Springer, 1981

About this Item

Print on Demand pp. 216 67:B&W 6.69 x 9.61 in or 244 x 170 mm (Pinched Crown) Perfect Bound on White w/Gloss Lam.

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Bibliographic Details

• Title: Robust Methods and Asymptotic Theory in Nonlinear Econometrics
• Publisher: Springer
• Publication Date: 1981
• Language: English
• ISBN 10: 3540108386
• ISBN 13: 9783540108382
• Binding: Soft cover
• Condition: New

About this title

Synopsis

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.