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Robust Methods and Asymptot...
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
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monografia Rebiun22332832 https://catalogo.rebiun.org/rebiun/record/Rebiun22332832 m o d cr mnu---uuaaa 121227s1981 gw os 000 0 eng 934980315 968663711 9783642455292 electronic bk.) 3642455298 electronic bk.) 9783540108382 3540108386 10.1007/978-3-642-45529-2 doi AU@ 000051703616 NZ1 14997757 NZ1 15312108 CBUC 991013456626906708 CBUC 991003832405606714 CBUC 991001069364706712 CBUC 991011079293206709 AU@ eng pn AU@ OCLCO OCLCQ GW5XE OCLCF UA@ COO OCLCQ OCLCO EBLCP OCLCQ UPM YDX UAB OCLCQ U3W LEAUB KCA bicssc BUS069030 bisacsh 330.1 23 Bierens, Herman J. Robust Methods and Asymptotic Theory in Nonlinear Econometrics by Herman J. Bierens Berlin, Heidelberg Springer Berlin Heidelberg 1981 Berlin, Heidelberg Berlin, Heidelberg Springer Berlin Heidelberg 1 online resource (ix, 198 pages) 1 online resource (ix, 198 pages) Text txt rdacontent computer c rdamedia online resource cr rdacarrier Lecture Notes in Economics and Mathematical Systems, Econometrics 0075-8442 192 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 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 Economics Economics- Statistics Economics Probability Theory and Stochastic Processes Economic Theory/Quantitative Economics/Mathematical Methods Statistics for Business, Management, Economics, Finance, Insurance Electronic books Statistics Print version 9783540108382 Lecture Notes in Economics and Mathematical Systems, Econometrics 192