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Journal of Mathematics
Volume 2013, Article ID 515830, 14 pages
http://dx.doi.org/10.1155/2013/515830
Research Article

On the Existence of Strongly Consistent Indirect Estimators When the Binding Function Is Compact Valued

Athens University of Economics and Business, Patision 76, 10434 Athens, Greece

Received 2 July 2013; Accepted 5 September 2013

Academic Editor: Mike Tsionas

Copyright © 2013 Stelios Arvanitis. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. A. A. Smith, “Estimating nonlinear time-series models using simulated vector autoregressions,” Journal of Applied Econometrics, vol. 8, no. 1, pp. 63–84, 1993. View at Publisher · View at Google Scholar
  2. C. Gourieroux, A. Monfort, and E. Renault, “Indirect inference,” Journal of Applied Econometrics, vol. 8, no. 1, pp. 85–118, 1993. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  3. R. A. Gallant and G. E. Tauchen, “Which Moments to Match?” Working Papers 95-20, Duke University, Department of Economic, 1995. View at Google Scholar
  4. G. Calzolari, G. Fiorentini, and E. Sentana, “Constrained indirect estimation,” Review of Economic Studies, vol. 71, no. 4, pp. 945–973, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. A. R. Gallant, D. Hsiehb, and G. Tauchen, “Estimation of stochastic volatility models with diagnostics,” Journal of Econometrics, vol. 81, no. 1, pp. 159–192, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  6. R. Garcia, E. Renault, and D. Veredas, “Estimation of stable distributions by indirect inference,” Journal of Econometrics, vol. 161, no. 2, pp. 325–337, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  7. T. G. Andersen, L. Benzoni, and J. Lund, “An empirical investigation of continuous-time equity return models,” Journal of Finance, vol. 57, no. 3, pp. 1239–1284, 2002. View at Publisher · View at Google Scholar · View at Scopus
  8. R. Bansal, A. R. Gallant, R. Hussey, and G. Tauchen, “Nonparametric estimation of structural models for high-frequency currency market data,” Journal of Econometrics, vol. 66, no. 1-2, pp. 251–287, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  9. C.-S. Chung and G. Tauchen, “Testing target-zone models using efficient method of moments,” Journal of Business & Economic Statistics, vol. 19, no. 3, pp. 255–277, 2001. View at Publisher · View at Google Scholar · View at MathSciNet
  10. A. Michaelides and S. Ng, “Estimating the rational expectations model of speculative storage: a Monte Carlo comparison of three simulation estimators,” Journal of Econometrics, vol. 96, no. 2, pp. 231–266, 2000. View at Publisher · View at Google Scholar · View at Scopus
  11. C. Gouriéroux, P. C. B. Phillips, and J. Yu, “Indirect inference for dynamic panel models,” Journal of Econometrics, vol. 157, no. 1, pp. 68–77, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  12. A. R. Gallant and J. R. Long, “Estimating stochastic differential equations efficiently by minimum chi-squared,” Biometrika, vol. 84, no. 1, pp. 125–141, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. C. Gourieroux and A. Monfort, Simulation-Based EconometricMethods, CORE Lectures, Ox. Un. Press, 1996.
  14. R. A. Chumacero, “Estimating ARMA models efficiently,” Studies in Nonlinear Dynamics and Econometrics, vol. 5, pp. 103–114, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  15. I. Ghysels, L. Khalaf, and C. Vodounou, “Simulation based inference in moving average models,” Annales d'Econommie et de Statistique, vol. 69, pp. 85–99, 2003. View at Google Scholar
  16. A. Demos and D. Kyriakopoulou, Edgeworth Expansions for the MLE And MM Estimators of An MA(1) Model, Communications in Statistics-Theory and Methods, Forthcoming, 2008.
  17. P. C. B. Phillips, “Folklore theorems, implicit maps, and indirect inference,” Econometrica, vol. 80, no. 1, pp. 435–454, 2012. View at Google Scholar · View at MathSciNet
  18. J. Dupačová and R. Wets, “Asymptotic behavior of statistical estimators and of optimal solutions of stochastic optimization problems,” The Annals of Statistics, vol. 16, no. 4, pp. 1517–1549, 1988. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. C. Hess, “Epi-convergence of sequences of normal integrands and strong consistency of the maximum likelihood estimator,” The Annals of Statistics, vol. 24, no. 3, pp. 1298–1315, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. P. Lachout, E. Liebscher, and S. Vogel, “Strong convergence of estimators as ϵn-minimisers of optimisation problems,” Annals of the Institute of Statistical Mathematics, vol. 57, no. 2, pp. 291–313, 2005. View at Publisher · View at Google Scholar · View at MathSciNet
  21. C. D. Aliprantis and K. C. Border, Infinite-Dimensional Analysis, Springer, Berlin, Germany, 2nd edition, 1999. View at MathSciNet
  22. I. Molchanov, Theory of Random Sets, Springer, London, UK, 2005. View at MathSciNet
  23. C. Choirat, C. Hess, and R. Seri, “A functional version of the Birkhoff ergodic theorem for a normal integrand: a variational approach,” The Annals of Probability, vol. 31, no. 1, pp. 63–92, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  24. D. Straumann, Estimation in Conditionally Heteroscedastic Time Series Models, vol. 181 of Lecture Notes in Statistics, Springer, Berlin, Germany, 2005. View at MathSciNet
  25. J. Pfanzagl, “On the measurability and consistency of minimum contrast estimates,” Metrika, vol. 14, pp. 249–272, 1969. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  26. T. R. Rockafellar and J.-B. Wetts, Variational Analysis, Springer, 1997.
  27. D. Applebaum, Lévy Processes and Stochastic Calculus, vol. 93 of Cambridge Studies in Advanced Mathematics, Cambridge University Press, Cambridge, UK, 2004. View at Publisher · View at Google Scholar · View at MathSciNet
  28. T. Bollerslev, “Generalized autoregressive conditional heteroskedasticity,” Journal of Econometrics, vol. 31, no. 3, pp. 307–327, 1986. View at Publisher · View at Google Scholar · View at MathSciNet
  29. S. Arvanitis and Al. Louka, “Limit Theory for the QMLE of the GQARCH(1,1) model,” Discussion Paper Series, Department of Economics, AUEB, 2012, http://www.econ.aueb.gr/DiscussionPapers2012.html.
  30. E. Klein and A. C. Thompson, Theory of Correspondences, Canadian Mathematical Society Series of Monographs and Advanced Texts, John Wiley & Sons, New York, NY, USA, 1984. View at MathSciNet
  31. R. T. Rockafellar and R. J.-B. Wets, “Variational systems, an introduction,” in Multifunctions and Integrands, vol. 1091, pp. 1–54, Springer, Berlin, Germany, 1984. View at Publisher · View at Google Scholar · View at MathSciNet
  32. Z. Artstein and J. A. Burns, “Integration of compact set-valued functions,” Pacific Journal of Mathematics, vol. 58, no. 2, pp. 297–307, 1975. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  33. R. van der Vaart, W. Aad, and J. A. Wellner, Weak Convergence and Empirical Processes, Springer, 2000.