zbMATH — the first resource for mathematics

A note on generalized empirical likelihood estimation of semiparametric conditional moment restriction models. (English) Zbl 1442.62073
Summary: This paper proposes an empirical likelihood-based estimation method for semiparametric conditional moment restriction models, which contain finite dimensional unknown parameters and unknown functions. We extend the results of S. G. Donald et al. [J. Econom. 117, No. 1, 55–93 (2003; Zbl 1022.62046)] by allowing unknown functions to be included in the conditional moment restrictions. We approximate unknown functions by a sieve method and estimate the finite dimensional parameters and unknown functions jointly. We establish consistency and derive the convergence rate of the estimator. We also show that the estimator of the finite dimensional parameters is $$\sqrt n$$-consistent, asymptotically normally distributed, and asymptotically efficient.

MSC:
 62G05 Nonparametric estimation 62F12 Asymptotic properties of parametric estimators
Full Text:
References:
 [1] Ai, C.; Chen, X., Efficient estimation of models with conditional moment restrictions containing unknown functions, Econometrica, 71, 1795-1843, (2003) · Zbl 1154.62323 [2] Blundell, R.; Chen, X.; Kristensen, D., Semi-nonparametric IV estimation of shape-invariant Engel curves, Econometrica, 75, 1613-1669, (2007) · Zbl 1133.91461 [3] Carrasco, M.; Florens, J.-P., Generalization of GMM to a continuum of moment conditions, Econometric Theory, 16, 797-834, (2000) · Zbl 0968.62028 [4] Chamberlain, G., Asymptotic efficiency in estimation with conditional moment restrictions, Journal of Econometrics, 34, 305-334, (1987) · Zbl 0618.62040 [5] Chen, X.; Pouzo, D., Efficient estimation of semiparametric conditional moment models with possibly nonsmooth residuals, Journal of Econometrics, 152, 46-60, (2009) · Zbl 1431.62111 [6] Dominguez, M. A.; Lobato, I. N., Consistent estimation of models defined by conditional moment restrictions, Econometrica, 2004, 1601-1615, (2004) · Zbl 1141.91635 [7] Donald, S. G.; Imbens, G. W.; Newey, W. K., Empirical likelihood estimation and consistent tests with conditional moment restrictions, Journal of Econometrics, 117, 55-93, (2003) · Zbl 1022.62046 [8] Kitamura, Y.; Tripathi, G.; Ahn, H., Empirical likelihood-based inference in conditional moment restriction models, Econometrica, 72, 1667-1714, (2004) · Zbl 1142.62331 [9] Newey, W. K., Efficient instrumental variable estimation of nonlinear models, Econometrica, 58, 809-837, (1990) · Zbl 0728.62107 [10] Newey, W. K., Uniform convergence in probability and stochastic equicontinuity, Econometrica, 59, 1161-1167, (1991) · Zbl 0743.60012 [11] Newey, W. K.; Powell, J. L., Instrumental variable estimation of nonparametric models, Econometrica, 71, 1565-1578, (2003) · Zbl 1154.62415 [12] Newey, W. K.; Smith, R. J., Higher order properties of GMM and generalized empirical likelihood estimators, Econometrica, 72, 219-255, (2004) · Zbl 1151.62313 [13] Nishiyama, Y.; Liu, Q.; Sueishi, N.; Zerger, A.; Argent, R. M., Proceedings of International Congress on Modelling and Simulation, Semiparametric estimators for conditional moment restrictions containing nonparametric functions: Comparison of GMM and empirical likelihood procedures, 926-932, (2005) [14] Otsu, T., Empirical likelihood estimation of conditional moment restriction models with unknown functions, Econometric Theory, 27, 8-46, (2011) · Zbl 1207.62073 [15] Qin, J.; Lawless, J., Empirical likelihood and general estimating equations, Annals of Statistics, 22, 300-325, (1994) · Zbl 0799.62049 [16] Robinson, P. M., Asymptotically efficient estimation in the presence of heteroskedasticity of unknown form, Econometrica, 55, 875-891, (1987) · Zbl 0651.62107 [17] Shen, X.; Wong, W. H., Convergence rate of sieve estimates, Annals of Statistics, 22, 580-615, (1994) · Zbl 0805.62008 [18] Smith, R. J., Efficient information theoretic inference for conditional moment restrictions, Journal of Econometrics, 138, 430-460, (2006) · Zbl 1418.62126 [19] Zhang, J.; Gijbels, I., Sieve empirical likelihood and extensions of the generalized least squares, Scandinavian Journal of Statistics, 30, 1-24, (2003) · Zbl 1034.62036
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.