Robust Methods and Asymptotic Theory in Nonlinear Econometrics - H. J. Bierens

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Résumé :
\gamma ) dollars dollars.- 4.4.2 A consistent initial value.- 4.4.3 An upperbound of the variance matrix.- 4.4.4 A note on the symmetry assumption.- 5 Nonlinear Models with Lagged Dependent Variables.- 5.1 Stochastic stability.- 5.1.1 Stochastically stable linear autoregressive processes.- 5.1.2 Multivariate stochastically stable processes.- 5.1.3 Other examples of stochastically stable processes.- 5.2 Limit theorem for stochastically stable processes.- 5.2.1 A uniform weak law of large numbers.- 5.2.2 Martingales.- 5.2.3 Central limit theorem for stochastically stable martingale differences.- 5.3 Dynamic nonlinear regression models and implicit structural equations.- 5.3.1 Dynamic nonlinear regression models.- 5.3.2 Dynamic nonlinear implicit structural equations.- 5.4 Remarks on the stochastic stability concept.- 6 Some Applications.- 6.1 Applications of robust M-estimation.- 6.1.1 Municipal expenditure.- 6.1.2 An autoregressive model of money demand.- 6.2 An application of minimum information estimation.- References.

Sommaire:
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.