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|
|Contact details of provider:|| Postal: Waterloo, Ontario, N2L 3G1|
Phone: (519) 888-4567 ext 33695
Fax: (519) 725-0530
Web page: http://economics.uwaterloo.ca/
More information through EDIRC
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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, René & 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).
- 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.
- 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.
- Susanne M. Schennach, 2007. "Point estimation with exponentially tilted empirical likelihood," Papers 0708.1874, arXiv.org.
- 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.
- Berkowitz, Jeremy, 2001. "Generalized spectral estimation of the consumption-based asset pricing model," Journal of Econometrics, Elsevier, vol. 104(2), pages 269-288, September.
- 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.
- Yuichi Kitamura & Gautam Tripathi & Hyungtaik Ahn, 2001.
"Empirical Likelihood-Based Inference in Conditional Moment Restriction Models,"
CIRJE-F-124, CIRJE, Faculty of Economics, University of Tokyo.
- Yuichi Kitamura & Gautam Tripathi & Hyungtaik Ahn, 2004. "Empirical Likelihood-Based Inference in Conditional Moment Restriction Models," Econometrica, Econometric Society, vol. 72(6), pages 1667-1714, November.
- 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.
- Marine Carrasco & Rachidi Kotchoni, 2013.
"Efficient estimation using the Characteristic Function,"
CIRANO Working Papers
- Marine Carrasco & Rachidi Kotchoni, 2013. "Efficient Estimation Using the Characteristic Function," Working Papers hal-00867850, HAL.
When requesting a correction, please mention this item's handle: RePEc:wat:wpaper:1104. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Pat Gruber)
If references are entirely missing, you can add them using this form.