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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.
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.
This book presents some of the more recent developments in nonlinear time series, including Bayesian analysis and cointegration tests.
McrM has been an active research area for over 20 years and the previous conferences clearly showed a tremendous growth of interest. A variety of successful applications and recent developments of interactive computer software to support decision making confinn a sustained progress. We therefore decided to make our theme "Inlproving Decision Making in Organisations". '!he aim was to take stock of the impact of multicriteria concepts in organisations and to involve management practitioners from a wide range of backgrounds. To this end the conference was organised round five broad themes and papers were solicited on the following topics:- Psychology - how do individuals in practice use and relate to the methodologies. Organisation - how do our models fit into the decision making framework of real organisations. Application - how have the models been used in practice and what is the users view. Methodology - what are the new areas in model development. Related Areas - is there complementary work eg. Expert Systems which may be attempting to solve very similar problems. '!he call for papers produced an overwhelming response of over 100 papers. '!hey were from a variety of disciplines and applications, and we decided to devote approximately one day to each of the five areas. We are very impressed by the results which can be seen in this edited proceedings.
The author is indebted to the Alfred P. Sloan Foundation and to the Graduate School of the University of Minnesota for financial aid. This permitted visits with quite a few old Cowlespeople, reproduction of documents, and some reduction in teaching commitments. The many who responded with information and suggestions cannot be blamed for the shortcomings of the book. Faculty and staff at the Cowles Foundation were particularly helpful. Dori Clifton, Business Manager, and Karlee Gifford, Librarian, were always resourceful in locating people and documents. Michael Intrilgator, Leonid Hurwicz, and Martin Beckmann fur- Intriligator also nished perceptive comments on an earlier draft. obtained my access to the Marschak archives at UCLA. Wendy Williamson, the librarian at the Jacob C. Schmookler Library at the University of Minnesota cheerfully and efficiently handled lots of (sometimes vague) requests for reference materials and produced neat and timely drafts from very trying scratchpaper. Appropriate parts of my correspondence and some copies of documents will be placed in a Cowles Commission archive at the Cowles Foundation, Vale University.