Dovonon, Prosper (2008): Large sample properties of the threestep euclidean likelihood estimators under model misspecification.

PDF
MPRA_paper_40025.pdf Download (583kB)  Preview 
Abstract
This paper studies the threestep Euclidean likelihood (3S) estimator and its corrected version as proposed by Antoine, Bonnal and Renault (2007) in globally misspecified models. We establish that the 3S estimator stays √nconvergent and asymptotically Gaussian. The discontinuity in the shrinkage factor makes the analysis of the corrected3S estimator harder to carry out in misspecified models. We propose a slight modification to this factor to control its rate of divergence in case of misspecification. We show that the resulting modified3S estimator is also higher order equivalent to the maximum empirical likelihood (EL) estimator in well specified models and √nconvergent and asymptotically Gaussian in misspecified models. Its asymptotic distribution robust to misspecification is also provided. Because of these properties, both the 3S and the modified3S estimators could be considered as computationally attractive alternatives to the exponentially tilted empirical likelihood estimator proposed by Schennach (2007) which also is higher order equivalent to EL in well specified models and √nconvergent in misspecified models.
Item Type:  MPRA Paper 

Original Title:  Large sample properties of the threestep euclidean likelihood estimators under model misspecification 
Language:  English 
Keywords:  Misspecified models, Empirical likelihood, Threestep Euclidean likelihood 
Subjects:  C  Mathematical and Quantitative Methods > C0  General > C01  Econometrics 
Item ID:  40025 
Depositing User:  Prosper Dovonon 
Date Deposited:  12 Jul 2012 02:26 
Last Modified:  05 Dec 2016 20:36 
References:  [1] Altonji, J. and Segal, L. (1996). Small Sample Bias in Gmm estimation of Covariance Structures. Journal of Business & Economic Statistics 14 353–366. [2] Andersen, T. G. and Sørensen, B. E. (1996). Gmm Estimation of a Stochastic Volatility Model: A Monte Carlo Study. Journal of Business & Economic Statistics 14 328–352. [3] Antoine, B., Bonnal, H. and Renault, E. (2007). On the Efficient Use of the Informational Content of Estimating Equations: Implied Probabilities and Euclidean Empirical Likelihood. Journal of Econometrics 138 461487. [4] Back, K. and Brown, D. P. (1993). Implied Probabilities in Gmm Estimators. Econometrica 61 971975. [5] Baggerly, K. A. (1998). Empirical Likelihood as Goodnessoffit Measure. Biometrika 85 535547. [6] Brown, B. W. and Newey W. K. (2002). Generalized Method of Moments, Efficient Bootstrapping, and Improved Inference. Journal of Business & Economic Statistics 20 507517. [7] Chamberlain, G. (1987). Asymptotic Efficiency in Estimation with Conditional Moment Restrictions. Journal of Econometrics 34 305334. [8] Corcoran, S. A. (1998). Bartlett Adjustment of Empirical Discrepancy Statistics. Biometrika 85 967 972. [9] Davidson, J. (1994). Stochastic Limit Theory. Oxford University Press, Oxford. [10] Donald, G. S., Imbens G. W. and Newey W. K. (2002). Empirical Likelihood Estimation and Consistent Tests with Conditional Moment Restrictions. Journal of Econometrics 117 5593. [11] Dovonon, P. and Renault E. (2008). Gmm Overidentification Test with First Order Underidentification. Working Paper. [12] Guggenberger, P. (2008). Finite Sample Evidence Suggesting a Heavy Tail Problem of the Generalized Empirical Likelihood Estimator. Econometric Reviews 27:4 526541. [13] Hall, A. R. (2000). Covariance Matrix Estimation and the Power of the Overidentifying Restrictions Test. Econometrica 68 15171527. [14] Hall, A. R. and Inoue A. (2003). The Large Sample Behaviour of the Generalized Method of Moments Estimator in Misspecified Models. Journal of Econometrics 114 361394. [15] Hall, P. and Horowitz J. (1996). Bootstrap Critical Values for Tests Based on Generalized Method of Moment Estimators. Econometrica 64 891916. [16] Hansen, L. P., 1982. “Large Sample Properties of Generalized Method of Moments Estimators,” Econometrica, 50, 10291054. [17] Hansen, L. P., Heaton P. and Yaron A. (1996). FiniteSample Properties of Some Alternative Gmm Estimators. Journal of Business & Economic Statistics 14 362280. [18] Imbens, G. W. (1997). OneStep Estimators in Overidentified Generalized Method of Moments Estimator. Review of Economic Studies 64 359383. 43 [19] Imbens, W. G. and Spady R. H. (2002). Confidence Intervals in Generalized Method of Moments Models. Journal of Econometrics 107 8798. [20] Imbens, W. G., Spady R. H. and Johnson P. (1998). Information Theoretic Approaches to Inference in Moment Condition Models. Econometrica 66 333357. [21] Kan, R. and Robotti C. (2008). Model Comparison Using the HansenJagannathan Distance. Review of Financial Studies, Forthcoming. [22] Kitamura, Y. (1997). Empirical Likelihood Methods with Weakly Dependent Processes. Annals of Statistics 25 20842102. [23] Kitamura, Y. (2001). Asymptotic Optimality of Empirical Likelihood for Testing Moment Restrictions. Econometrica 69 16611672. [24] Kitamura, Y. (2006). Empirical Likelihood Methods in Econometrics: Theory and Practice. Cowles Foundation for Research in Economics, Yale University, Discussion paper No. 1569. [25] Kitamura, Y. and Stutzer M. (1997). An InformationTheorethic Alternative to Generalized Method of Moments Estimation. Econometrica 65 861874. [26] Kitamura, Y., Tripathi G. and Ahn H. (2004). Empirical Likelihoodbased Inference in Conditional Moment Restriction Models. Econometrica 72 16671714. [27] Magdalinos, A. M. and Symeonides S. D. (1996). A Reinterpretation of the Tests of Overidentifying Restrictions. Journal of Econometrics 73 325353. [28] Mykland, P. A. (1995). Dual Likelihood. Annals of Statistics 23 396421. [29] Newey, K. W. (1985). Generalized Method of Moments Specification Testing. Journal of Econometrics 29 229256. [30] Newey, K. W. and McFadden D. (1994). Large Sample Estimation and Hypothesis. Handbook of Econometrics, IV, Edited by R. F. Engle and D. L. McFadden, 21122245. [31] Newey, K. W. and Smith R. J. (2004). Higher Order Properties of Gmm and Generalized Empirical Likelihood Estimators. Econometrica 72 219255. [32] Newey, K. W. and West K. D. (1987). A Simple, Positive SemiDefinite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix. Econometrica 55 703708. [33] Owen, A. (1990). Empirical Likelihood Ratio Confident Regions. Annals of Statistics 18 90120. [34] Owen, A. (2001). Empirical Likelihood. Chapman & Hall, New York. [35] Qin, J. and Lawless J. (1994). Empirical Likelihood and General Estimating Equations. Annals of Statistics 22 300325. [36] Ramalho, J. S. and Smith R. J. (2002). Generalized Empirical Likelihood NonNested Tests. Journal of Econometrics 107 99125. [37] Robinson, P. M. (1988). The Stochastic Difference Between Econometric Statistics. Econometrica 56 531548. [38] Schennach, S. M. (2007). Point Estimation with Exponentially Tilted Empirical Likelihood. Annals of Statistics 35 634672. [39] White, H. 1982. Maximum Likelihood Estimation of Misspecified Models. Econometrica 50 125. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/40025 