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An Introduction to Econometric Applications of Functional Limit Theory for Dependent Random Variables

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Abstract

This paper discusses some uses econometrics of functional limit theory for dependent random variables. Attention is focused on empirical process-type results rather than partial sum results that are prevalent in unit root econometrics. Examples considered include nonstandard parametric hypotheses tests and semiparametric estimation. The application of bracketing functional limit results is discussed in some detail.

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File URL: http://cowles.econ.yale.edu/P/cd/d10a/d1020.pdf
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Bibliographic Info

Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1020.

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Length: 40 pages
Date of creation: May 1992
Date of revision:
Publication status: Published in Econometric Review (1993), 12(2): 183-216
Handle: RePEc:cwl:cwldpp:1020

Note: CFP 837.
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Postal: Yale University, Box 208281, New Haven, CT 06520-8281 USA
Phone: (203) 432-3702
Fax: (203) 432-6167
Web page: http://cowles.econ.yale.edu/
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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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Keywords: Hypothesis tests; semiparametric estimation;

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References

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  1. Bera, A.K. & Higgins, M.L., 1990. "A Test For Conditional Heterskedasticity In Time Series Midels," University of Western Ontario, The Centre for the Study of International Economic Relations Working Papers 9003, University of Western Ontario, The Centre for the Study of International Economic Relations.
  2. Pakes, Ariel & Olley, Steven, 1995. "A limit theorem for a smooth class of semiparametric estimators," Journal of Econometrics, Elsevier, vol. 65(1), pages 295-332, January.
  3. Donald W.K. Andrews & Werner Ploberger, 1992. "Optimal Tests When a Nuisance Parameter Is Present Only Under the Alternative," Cowles Foundation Discussion Papers 1015, Cowles Foundation for Research in Economics, Yale University.
  4. Andrews, Donald W K, 1993. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Econometrica, Econometric Society, vol. 61(4), pages 821-56, July.
  5. Terasvirta, T & Anderson, H M, 1992. "Characterizing Nonlinearities in Business Cycles Using Smooth Transition Autoregressive Models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 7(S), pages S119-36, Suppl. De.
  6. Newey, Whitney K, 1991. "Uniform Convergence in Probability and Stochastic Equicontinuity," Econometrica, Econometric Society, vol. 59(4), pages 1161-67, July.
  7. Yoon-Jae Whang & Donald W.K. Andrews, 1991. "Tests of Specification for Parametric and Semiparametric Models," Cowles Foundation Discussion Papers 968, Cowles Foundation for Research in Economics, Yale University.
  8. Simon M. Potter, 1993. "A Nonlinear Approach to U.S. GNP," UCLA Economics Working Papers 693, UCLA Department of Economics.
  9. Andrews, Donald W. K., 1991. "An empirical process central limit theorem for dependent non-identically distributed random variables," Journal of Multivariate Analysis, Elsevier, vol. 38(2), pages 187-203, August.
  10. Hansen, B.E., 1991. "The Likelihood Test Under Non-Standard Conditions: Testing the Markov Trend Model of GNP," RCER Working Papers 279, University of Rochester - Center for Economic Research (RCER).
  11. repec:cup:etheor:v:8:y:1992:i:2:p:241-57 is not listed on IDEAS
  12. Donald W.K. Andrews, 1990. "Generic Uniform Convergence," Cowles Foundation Discussion Papers 940, Cowles Foundation for Research in Economics, Yale University.
  13. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-84, March.
  14. Hansen, B.E., 1991. "Inference when a Nuisance Parameter is Not Identified Under the Null Hypothesis," RCER Working Papers 296, University of Rochester - Center for Economic Research (RCER).
  15. Peter C.B. Phillips & Victor Solo, 1989. "Asymptotics for Linear Processes," Cowles Foundation Discussion Papers 932, Cowles Foundation for Research in Economics, Yale University.
  16. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
  17. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
  18. Robinson, P M, 1987. "Asymptotically Efficient Estimation in the Presence of Heteroskedasticity of Unknown Form," Econometrica, Econometric Society, vol. 55(4), pages 875-91, July.
  19. Andrews, Donald W.K., 1995. "Nonparametric Kernel Estimation for Semiparametric Models," Econometric Theory, Cambridge University Press, vol. 11(03), pages 560-586, June.
  20. Robert B. Davies, 2002. "Hypothesis testing when a nuisance parameter is present only under the alternative: Linear model case," Biometrika, Biometrika Trust, vol. 89(2), pages 484-489, June.
  21. Yatchew, Adonis John, 1992. "Nonparametric Regression Tests Based on Least Squares," Econometric Theory, Cambridge University Press, vol. 8(04), pages 435-451, December.
  22. Donald W.K. Andrews, 1989. "Asymptotics for Semiparametric Econometric Models: I. Estimation," Cowles Foundation Discussion Papers 908R, Cowles Foundation for Research in Economics, Yale University, revised Aug 1990.
  23. Horowitz, Joel L, 1992. "A Smoothed Maximum Score Estimator for the Binary Response Model," Econometrica, Econometric Society, vol. 60(3), pages 505-31, May.
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Citations

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Cited by:
  1. Čížek, Pavel, 2008. "General Trimmed Estimation: Robust Approach To Nonlinear And Limited Dependent Variable Models," Econometric Theory, Cambridge University Press, vol. 24(06), pages 1500-1529, December.
  2. Valentina Corradi & Norman R. Swanson, 2003. "Bootstrap Specification Tests for Diffusion Processes," Departmental Working Papers 200321, Rutgers University, Department of Economics.
  3. Donald W.K. Andrews, 1996. "A Stopping Rule for the Computation of Generalized Method of Moments Estimators," Cowles Foundation Discussion Papers 1120, Cowles Foundation for Research in Economics, Yale University.
  4. Corradi, Valentina & Swanson, Norman R., 2006. "Bootstrap conditional distribution tests in the presence of dynamic misspecification," Journal of Econometrics, Elsevier, vol. 133(2), pages 779-806, August.
  5. Bruce E. Hansen, 1994. "Stochastic Equicontinuity for Unbounded Dependent Heterogeneous Arrays," Boston College Working Papers in Economics 295., Boston College Department of Economics.
  6. Cizek, P., 2006. "Efficient Robust Estimation of Regression Models (Replaced by DP 2007-87)," Discussion Paper 2006-8, Tilburg University, Center for Economic Research.
  7. Cizek, P., 2007. "General Trimmed Estimation: Robust Approach to Nonlinear and Limited Dependent Variable Models (Replaced by DP 2007-65)," Discussion Paper 2007-1, Tilburg University, Center for Economic Research.

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