Generalized empirical likelihood for a continuum of moment conditions
This paper extends the generalized empirical likelihood method to the case in which the moment conditions are defined on a continuum (CGEL). We show, for the iid case, that CGEL is asymptotically equivalent at the first order to the generalized method of moments for a continuum (CGMM) developed by Carrasco and Florens (2000). Because the system of equations that we need to solve becomes singular when the number of moment conditions converges to infinity, we treat CGEL as a nonlinear ill-posed problem and obtain the solution using the regularized Gauss-Newton method. This numerical algorithm is a fast and relatively easy way to compute the regularized Tikhonov solution to nonlinear ill-posed problems in function spaces. In order to compare the properties of CGEL and CGMM, we then perform a numerical study in which we estimate the parameters of a stable distribution using moment conditions based on the characteristic function. The results show that CGEL outperforms CGMM in most cases according to the root mean squared error criterion.
|Date of creation:||Oct 2011|
|Date of revision:||Oct 2011|
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- Carrasco, Marine & Florens, Jean-Pierre, 2000. "Generalization Of Gmm To A Continuum Of Moment Conditions," Econometric Theory, Cambridge University Press, vol. 16(06), pages 797-834, December.
- Marine Carrasco & Rachidi Kotchoni, 2013.
"Efficient Estimation Using the Characteristic Function,"
- Marine Carrasco & Rachidi Kotchoni, 2013. "Efficient estimation using the Characteristic Function," CIRANO Working Papers 2013s-22, CIRANO.
- Anatolyev, Stanislav & Gospodinov, Nikolay, 2011.
"Specification Testing In Models With Many Instruments,"
Cambridge University Press, vol. 27(02), pages 427-441, April.
- Stanislav Anatolyev & Nikolay Gospodinov, 2008. "Specification Testing in Models with Many Instruments," Working Papers w0124, Center for Economic and Financial Research (CEFIR).
- Donald, Stephen G. & Imbens, Guido W. & Newey, Whitney K., 2003. "Empirical likelihood estimation and consistent tests with conditional moment restrictions," Journal of Econometrics, Elsevier, vol. 117(1), pages 55-93, November.
- Garcia, René & Renault, Eric & Veredas, David, 2011.
"Estimation of stable distributions by indirect inference,"
Journal of Econometrics,
Elsevier, vol. 161(2), pages 325-337, April.
- GARCIA, RenÃ© & RENAULT, Eric & VEREDAS, David, 2006. "Estimation of stable distributions by indirect inference," CORE Discussion Papers 2006112, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Yuichi Kitamura & Gautam Tripathi & Hyungtaik Ahn, 2004.
"Empirical Likelihood-Based Inference in Conditional Moment Restriction Models,"
Econometric Society, vol. 72(6), pages 1667-1714, November.
- Yuichi Kitamura & Gautam Tripathi & Hyungtaik Ahn, 2001. "Empirical Likelihood-Based Inference in Conditional Moment Restriction Models," CIRJE F-Series CIRJE-F-124, CIRJE, Faculty of Economics, University of Tokyo.
- Berkowitz, Jeremy, 2001. "Generalized spectral estimation of the consumption-based asset pricing model," Journal of Econometrics, Elsevier, vol. 104(2), pages 269-288, September.
- Hélène Bonnal & Éric Renault, 2004.
"On the Efficient Use of the Informational Content of Estimating Equations: Implied Probabilities and Euclidean Empirical Likelihood,"
CIRANO Working Papers
- Antoine, Bertille & Bonnal, Helene & Renault, Eric, 2007. "On the efficient use of the informational content of estimating equations: Implied probabilities and Euclidean empirical likelihood," Journal of Econometrics, Elsevier, vol. 138(2), pages 461-487, June.
- Carrasco, Marine & Chernov, Mikhail & Florens, Jean-Pierre & Ghysels, Eric, 2007. "Efficient estimation of general dynamic models with a continuum of moment conditions," Journal of Econometrics, Elsevier, vol. 140(2), pages 529-573, October.
- Carrasco, Marine & Florens, Jean-Pierre & Renault, Eric, 2007. "Linear Inverse Problems in Structural Econometrics Estimation Based on Spectral Decomposition and Regularization," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 77 Elsevier.
- Susanne M. Schennach, 2007. "Point estimation with exponentially tilted empirical likelihood," Papers 0708.1874, arXiv.org.
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