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Adaptive estimation of regression models via moment restrictions. (English) Zbl 0686.62045
Summary: This paper considers adaptive estimation of regression models by means of generalized method of moments estimators. Two models are considered, one with an i.i.d. disturbance that is independent of the regressors and one with a conditionally symmetric but (possibly) heteroskedastic disturbance. For both cases the paper develops linearized estimators that are asymptotically efficient if the number and variety of moment conditions are allowed to grow at an appropriate rate with the sample size. In the general symmetric case no other adaptive estimator has yet been proposed.
Also, results of a small Monte Carlo study indicate that in the independence case the small sample performance of the generalized method of moments estimator can be quite good vis-a-vis other estimators previously proposed.

62J05 Linear regression; mixed models
62P20 Applications of statistics to economics
Full Text: DOI
[1] Amemiya, T.: The maximum likelihood and nonlinear three-stage least squares estimator inthe general nonlinear simultaneous equations model. Econometrica 45, 955-968 (1977) · Zbl 0359.62026
[2] Bartle, R. G.: The elements of integration. (1966) · Zbl 0146.28201
[3] Beran, R.: Adaptive estimates for autoregressive processes. Annals of the institute of statistical mathematics 26, 77-89 (1976) · Zbl 0362.62093
[4] Bickle, P.: On adaptive estimation. Annals of statistics 10, 647-671 (1982) · Zbl 0489.62033
[5] Billingsley, P.: Probability and measure. (1979) · Zbl 0411.60001
[6] Carroll, R. J.: Adapting for heteroskedasticity in linear models. Annals of statistics 10, 1224-1233 (1982) · Zbl 0571.62058
[7] Chamberlain, G.: Comment on adaptive estimation of nonlinear regression models. Econometric reviews 3, 197-199 (1984)
[8] Chamberlain, G.: Asymptotic efficiency in estimation with conditional moment restrictions. Journal of econometrics 34, 305-334 (1987) · Zbl 0618.62040
[9] Fraud, G.: Orthogonal polynomials. (1971)
[10] Gallant, A. R.: Explicit estimators of parametric functions in nonlinear regression. Journal of the American statistical association 75, 182-193 (1980) · Zbl 0425.62045
[11] Gregory, R. T.; Karney, D. L.: A collection of matrices for testing computational algorithms. (1969) · Zbl 0195.44803
[12] Hajek, J.; Sidak, Z.: Theory of rank tests. (1967) · Zbl 0161.38102
[13] Hansen, L. P.: Large sample properties of generalized method of moments estimators. Econometrica 50, 1029-1054 (1982) · Zbl 0502.62098
[14] Hansen, L. P.: Using martingale difference approximations to obtain covariance matrix bounds for generalized method of moments estimators. (1985)
[15] Hsieh, D.; Manski, C.: Monte-Carlo evidence on adaptive maximum likelihood estimation of a regression. Annals of statistics (1987) · Zbl 0621.62034
[16] Macurdy, T. E.: Using information on the moments of the disturbance to increase the efficiency of estimation. (1982)
[17] Manski, C.: Adaptive estimation of nonlinear regression models. Econometric reviews 3, 145-194 (1984) · Zbl 0607.62034
[18] Newey, W. K.: Nearly efficient moment restriction estimation of regression models with nonnormal disturbances. Econometric research program memo. No. 315 (1984)
[19] Newey, W. K.: Generalized method of moments specification testing. Journal of econometrics 29, 229-256 (1985) · Zbl 0606.62132
[20] Newey, W. K.: Efficient estimation of models with conditional moment restrictions. (1987) · Zbl 0635.62113
[21] Newey, W. K.: Efficient estimation of semiparametric models via moment restrictions. (1987)
[22] Newey, W. K.: Efficient estimation of tobit models under symmetry. (1987) · Zbl 0635.62113
[23] Newey, W.K., J.L. Powell, Efficient estimation of linear and type I censored regression models under conditional quantile restrictions, Econometric research program memo. no. 331 (Princeton University, Princeton, NJ).
[24] Robinson, P.: Asymptotically efficient estimation in the presence of heteroskedasticity of unknown form. Econometrica 55, 875-891 (1987) · Zbl 0651.62107
[25] White, H.: Instrumental variable regression with independent observations. Econometrica 50, 483-499 (1982) · Zbl 0518.62094
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