Econometric simultaneous equation models play an important role in making economic policies, analyzing economic structure and economic forecasting. This paper presents local linear estimators by TSLS with variable ban...Econometric simultaneous equation models play an important role in making economic policies, analyzing economic structure and economic forecasting. This paper presents local linear estimators by TSLS with variable bandwidth for every structural equation in semi-parametric simultaneous equation models in econometrics. The properties under large sample size were studied by using the asymptotic theory when all variables were random. The results show that the estimators of the parameters have consistency and asymptotic normality, and their convergence rates are equal to n^-1/2. And the estimator of the nonparametric function has the consistency and asymptotic normality in interior points and its rate of convergence is equal to the optimal convergence rate of the nonparametric function estimation.展开更多
A robust version of local linear regression smoothers augmented with variable bandwidth is studied. The proposed method inherits the advantages of local polynomial regression and overcomes the shortcoming of lack of r...A robust version of local linear regression smoothers augmented with variable bandwidth is studied. The proposed method inherits the advantages of local polynomial regression and overcomes the shortcoming of lack of robustness of leastsquares techniques. The use of variable bandwidth enhances the flexibility of the resulting local M-estimators and makes them possible to cope well with spatially inhomogeneous curves, heteroscedastic errors and nonuniform design densities. Under appropriate regularity conditions, it is shown that the proposed estimators exist and are asymptotically normal. Based on the robust estimation equation, one-step local M-estimators are introduced to reduce computational burden. It is demonstrated that the one-step local M-estimators share the same asymptotic distributions as the fully iterative M-estimators, as long as the initial estimators are good enough. In other words, the onestep local M-estimators reduce significantly the computation cost of the fully iterative M-estimators without deteriorating their performance. This fact is also illustrated via simulations.展开更多
基金This project is supported by National Natural Science Foundation of China （70371025）
文摘Econometric simultaneous equation models play an important role in making economic policies, analyzing economic structure and economic forecasting. This paper presents local linear estimators by TSLS with variable bandwidth for every structural equation in semi-parametric simultaneous equation models in econometrics. The properties under large sample size were studied by using the asymptotic theory when all variables were random. The results show that the estimators of the parameters have consistency and asymptotic normality, and their convergence rates are equal to n^-1/2. And the estimator of the nonparametric function has the consistency and asymptotic normality in interior points and its rate of convergence is equal to the optimal convergence rate of the nonparametric function estimation.
文摘A robust version of local linear regression smoothers augmented with variable bandwidth is studied. The proposed method inherits the advantages of local polynomial regression and overcomes the shortcoming of lack of robustness of leastsquares techniques. The use of variable bandwidth enhances the flexibility of the resulting local M-estimators and makes them possible to cope well with spatially inhomogeneous curves, heteroscedastic errors and nonuniform design densities. Under appropriate regularity conditions, it is shown that the proposed estimators exist and are asymptotically normal. Based on the robust estimation equation, one-step local M-estimators are introduced to reduce computational burden. It is demonstrated that the one-step local M-estimators share the same asymptotic distributions as the fully iterative M-estimators, as long as the initial estimators are good enough. In other words, the onestep local M-estimators reduce significantly the computation cost of the fully iterative M-estimators without deteriorating their performance. This fact is also illustrated via simulations.
