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Monte Carlo Tests with Nuisance Parameters: A General Approach to Finite-Sample Inference and Nonstandard Asymptotics

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  • DUFOUR, Jean-Marie

Abstract

The technique of Monte Carlo (MC) tests [Dwass (1957), Barnard (1963)] provides an attractive method of building exact tests from statistics whose finite sample distribution is intractable but can be simulated (provided it does not involve nuisance parameters). We extend this method in two ways: first, by allowing for MC tests based on exchangeable possibly discrete test statistics; second, by generalizing the method to statistics whose null distributions involve nuisance parameters (maximized MC tests, MMC). Simplified asymptotically justified versions of the MMC method are also proposed and it is shown that they provide a simple way of improving standard asymptotics and dealing with nonstandard asymptotics (e.g., unit root asymptotics). Parametric bootstrap tests may be interpreted as a simplified version of the MMC method (without the general validity properties of the latter).

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Bibliographic Info

Paper provided by Centre interuniversitaire de recherche en économie quantitative, CIREQ in its series Cahiers de recherche with number 03-2005.

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Length: 45 pages
Date of creation: 2005
Date of revision:
Handle: RePEc:mtl:montec:03-2005

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Keywords: Monte Carlo test; maximized monte Carlo test; finite sample test; exact test; nuisance parameter; bounds; bootstrap; parametric bootstrap; simulated annealing; asymptotics; nonstandard asymptotic distribution;

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  1. Jean-Marie Dufour & Tarek Jouini, 2005. "Finite-Sample Simulation-Based Inference in VAR Models with Applications to Order Selection and Causality Testing," CIRANO Working Papers 2005s-26, CIRANO.
  2. Jean-Marie Dufour & Abdeljelil Farhat & Lucien Gardiol & Lynda Khalaf, 1998. "Simulation-based finite sample normality tests in linear regressions," Econometrics Journal, Royal Economic Society, vol. 1(Conferenc), pages C154-C173.
  3. Dufour, Jean-Marie, 1989. "Nonlinear Hypotheses, Inequality Restrictions, and Non-nested Hypotheses: Exact Simultaneous Tests in Linear Regressions," Econometrica, Econometric Society, vol. 57(2), pages 335-55, March.
  4. Atsushi Inoue & Lutz Kilian, 2002. "Bootstrapping Autoregressive Processes with Possible Unit Roots," Econometrica, Econometric Society, vol. 70(1), pages 377-391, January.
  5. Dufour, Jean-Marie, 1990. "Exact Tests and Confidence Sets in Linear Regressions with Autocorrelated Errors," Econometrica, Econometric Society, vol. 58(2), pages 475-94, March.
  6. Marc Hallin & Jean-Marie Dufour & Ivan Mizera, 1998. "Generalized run tests for heteroscedastic time series," ULB Institutional Repository 2013/2077, ULB -- Universite Libre de Bruxelles.
  7. Tauchen, George E. & Gallant, A. Ronald, 1995. "Which Moments to Match," Working Papers 95-20, Duke University, Department of Economics.
  8. Campbell, Bryan & Dufour, Jean-Marie, 1997. "Exact Nonparametric Tests of Orthogonality and Random Walk in the Presence of a Drift Parameter," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 38(1), pages 151-73, February.
  9. Stinchcombe, Maxwell B & White, Halbert, 1992. "Some Measurability Results for Extrema of Random Functions over Random Sets," Review of Economic Studies, Wiley Blackwell, vol. 59(3), pages 495-514, July.
  10. Alexander Benkwitz & Michael Neumann & Helmut Lutekpohl, 2000. "Problems related to confidence intervals for impulse responses of autoregressive processes," Econometric Reviews, Taylor & Francis Journals, vol. 19(1), pages 69-103.
  11. Inoue, Atsushi & Kilian, Lutz, 2003. "The Continuity Of The Limit Distribution In The Parameter Of Interest Is Not Essential For The Validity Of The Bootstrap," Econometric Theory, Cambridge University Press, vol. 19(06), pages 944-961, December.
  12. Kiviet, Jan F. & Dufour, Jean-Marie, 1997. "Exact tests in single equation autoregressive distributed lag models," Journal of Econometrics, Elsevier, vol. 80(2), pages 325-353, October.
  13. Joel L. Horowitz, 1996. "Bootstrap Methods in Econometrics: Theory and Numerical Performance," Econometrics 9602009, EconWPA, revised 05 Mar 1996.
  14. Jouneau-Sion, Frederic & Torres, Olivier, 2006. "MMC techniques for limited dependent variables models: Implementation by the branch-and-bound algorithm," Journal of Econometrics, Elsevier, vol. 133(2), pages 479-512, August.
  15. Goffe, William L. & Ferrier, Gary D. & Rogers, John, 1994. "Global optimization of statistical functions with simulated annealing," Journal of Econometrics, Elsevier, vol. 60(1-2), pages 65-99.
  16. Dufour, J.M. & Kiviet, J.F., 1995. "Exact Inference Methods for First-Order Autoregressive Distributed Lag Models," Cahiers de recherche 9547, Universite de Montreal, Departement de sciences economiques.
  17. Dufour, Jean-Marie & Jasiak, Joann, 2001. "Finite Sample Limited Information Inference Methods for Structural Equations and Models with Generated Regressors," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 42(3), pages 815-43, August.
  18. Daniel McFadden, 1987. "A Method of Simulated Moments for Estimation of Discrete Response Models Without Numerical Integration," Working papers 464, Massachusetts Institute of Technology (MIT), Department of Economics.
  19. repec:cup:etheor:v:12:y:1996:i:4:p:657-81 is not listed on IDEAS
  20. Donald W. K. Andrews, 2000. "Inconsistency of the Bootstrap when a Parameter Is on the Boundary of the Parameter Space," Econometrica, Econometric Society, vol. 68(2), pages 399-406, March.
  21. Keane, Michael, 1993. "Simulation estimation for panel data models with limited dependent variables," MPRA Paper 53029, University Library of Munich, Germany.
  22. Dufour, Jean-Marie & Kiviet, Jan F., 1996. "Exact tests for structural change in first-order dynamic models," Journal of Econometrics, Elsevier, vol. 70(1), pages 39-68, January.
  23. Lynda Khalaf & Jean-Marie Dufour, 2004. "Simulation-Based Finite-Sample Inference in Simultaneous Equations," Econometric Society 2004 North American Summer Meetings 239, Econometric Society.
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