Advanced Search
MyIDEAS: Login to save this paper or follow this series

Simulation Based Finite and Large Sample Tests in Multivariate Regressions

Contents:

Author Info

  • Jean-Marie Dufour

    ()

  • Lynda Khalaf

Abstract

In the context of multivariate linear regression (MLR) models, it is well known that commonly employed asymptotic test criteria are seriously biased towards overrejection. In this paper, we propose a generalmethod for constructing exact tests of possible nonlinear hypotheses on the coefficients of MLR systems. For the case of uniform linear hypotheses, we present exact distributional invariance results concerning several standard test criteria. These include Wilks' likelihood ratio (LR) criterion as well as trace and maximum root criteria. The normality assumption is not necessarily for most of the results to hold. Implications for inference are two-fold. First, invariance to nuisance parameters entails that the technique of Monte Carlo tests can be applied on all these statistics to obtain exact tests of uniform linear hypotheses. Second, the invariance property of the latter statistic is exploited to derive general nuisance-parameter-free bounds on the distribution of the LR statistic for arbitrary hypotheses. Even though it may be difficult to compute these bounds analytically, they can easily be simulated, hence yielding exact bounds Monte Carlo tests. Illustrative simulation experiments show that the bounds are sufficiently tight to provide conclusive results with a high probability. Our findings illustrate the value of the bounds as a tool to be used in conjunction with more traditional simulation-based test methods (e.g., the parametric bootstrap) which may be applied when the bounds are not conclusive. Dans le contexte des modèles de régression multivariés (MLR), il est bien connu que les tests asymptotiques usuels tendent à rejeter trop souvent les hypothèse considérées. Dans cet article, nous proposons une méthode générale qui permet de construire des tests exacts pour des hypothèses possiblement non linéaires sur les coefficients de tels modèles. Pour le cas des hypothèse uniformes linéaires, nous présentons des résultats sur la distribution exacte de plusieurs statistiques de test usuelles. Ces dernières incluent le critère du quotient de vraisemblance (Wilks), de même que les critères de la trace et de la racine maximale. L'hypothèse de normalité des erreurs n'est pas requise pour la plupart des résultats présentés. Ceux-ci ont deux types de conséquences pour l'inférence statistique. Premièrement, l'invariance par rapport aux paramètres de nuisance signifie que l'on peut appliquer la technique des tests de Monte Carlo afin de construire des tests exacts pour les hypothèses uniformes linéaires. Deuxième-ment, nous montrons comment exploiter cette propriété afin d'obtenir des bornes sans paramètres de nuisance sur la distribution des statistiques de quotient de vraisemblance pour des hypothèses générales. Même si les bornes ne sont pas faciles à calculer par des moyens analytiques, on peut les simuler aisément et ainsi effectuer des tests de Monte Carlo à bornes. Nous présentons une expérience de simulation qui montre que ces bornes sont suffisamment serrées pour fournir des résultats concluants avec une forte probabilité. Nos résultats démontrent la valeur de ces bornes comme instrument à utiliser conjointement avec des méthodes d'inférence simulée plus traditionnelles (telles que le bootstrap paramétrique) que l'on peut appliquer lorsque le test à borne n'est pas concluant.

Download Info

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
File URL: http://www.cirano.qc.ca/pdf/publication/2000s-15.pdf
Download Restriction: no

Bibliographic Info

Paper provided by CIRANO in its series CIRANO Working Papers with number 2000s-15.

as in new window
Length:
Date of creation: 01 May 2000
Date of revision:
Handle: RePEc:cir:cirwor:2000s-15

Contact details of provider:
Postal: 2020 rue University, 25e étage, Montréal, Quéc, H3A 2A5
Phone: (514) 985-4000
Fax: (514) 985-4039
Email:
Web page: http://www.cirano.qc.ca/
More information through EDIRC

Related research

Keywords: Multivariate linear regression; seemingly unrelated regressions; uniform linear hypothesis; Monte Carlo test; bounds test. Nonlinear hypothesis; finite sample test; exact test; bootstrap; Modèle de régression multivarié; régressions empilées; hypothès linéaire uniforme; test de Monte Caro; test à borne; hypothèse non linéaire; test à distance finie; test exact; bootstrap;

Other versions of this item:

Find related papers by JEL classification:

References

References listed on IDEAS
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.:
as in new window
  1. Atkinson, Scott E. & Wilson, Paul W., 1992. "The Bias of Bootstrapped Versus Conventional Standard Errors in the General Linear and SUR Models," Econometric Theory, Cambridge University Press, vol. 8(02), pages 258-275, June.
  2. Evans, G B A & Savin, N E, 1982. "Conflict among the Criteria Revisited: The W, LR and LM Tests," Econometrica, Econometric Society, vol. 50(3), pages 737-48, May.
  3. Davidson, Russell & MacKinnon, James G., 1993. "Estimation and Inference in Econometrics," OUP Catalogue, Oxford University Press, number 9780195060119, September.
  4. Laitinen, Kenneth, 1978. "Why is demand homogeneity so often rejected?," Economics Letters, Elsevier, vol. 1(3), pages 187-191.
  5. DUFOUR, Jean-Marie & FARHAT, Abdeljelil & GARDIOL, Lucien, 1998. "Simulation-Based Finite-Sample Normality Tests in Linear Regressions," Cahiers de recherche 9811, Universite de Montreal, Departement de sciences economiques.
  6. 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.
  7. Jean-Marie Dufour & Lynda Khalaf, 1999. "Simulation Based Finite- and Large-Sample Inference Methods in Simultaneous Equations," Computing in Economics and Finance 1999 824, Society for Computational Economics.
  8. Affleck-Graves, John & McDonald, Bill, 1990. "Multivariate Tests of Asset Pricing: The Comparative Power of Alternative Statistics," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 25(02), pages 163-185, June.
  9. Meisner, James F., 1979. "The sad fate of the asymptotic Slutsky symmetry test for large systems," Economics Letters, Elsevier, vol. 2(3), pages 231-233.
  10. Theil, Henri & Shonkwiler, J. S. & Taylor, Timothy G., 1985. "A Monte Carlo test of Slutsky symmetry," Economics Letters, Elsevier, vol. 19(4), pages 331-332.
  11. Stambaugh, Robert F., 1982. "On the exclusion of assets from tests of the two-parameter model : A sensitivity analysis," Journal of Financial Economics, Elsevier, vol. 10(3), pages 237-268, November.
  12. Cribari-Neto, Francisco & Zarkos, Spyros G, 1997. "Finite-Sample Adjustments for Homogeneity and Symmetry Tests in Systems of Demand Equations: A Monte Carlo Evaluation," Computational Economics, Society for Computational Economics, vol. 10(4), pages 337-51, November.
  13. Attfield, C. L. F., 1995. "A Bartlett adjustment to the likelihood ratio test for a system of equations," Journal of Econometrics, Elsevier, vol. 66(1-2), pages 207-223.
  14. Berndt, Ernst R & Savin, N Eugene, 1977. "Conflict among Criteria for Testing Hypotheses in the Multivariate Linear Regression Model," Econometrica, Econometric Society, vol. 45(5), pages 1263-77, July.
  15. Taylor, Timothy G. & Shonkwiler, J. S. & Theil, Henri, 1986. "Monte Carlo and bootstrap testing of demand homogeneity," Economics Letters, Elsevier, vol. 20(1), pages 55-57.
  16. Russell Davidson & James G. MacKinnon, 2001. "Bootstrap Tests: How Many Bootstraps?," Working Papers 1036, Queen's University, Department of Economics.
  17. Davidson, R. & Mackinnon, J.G., 1997. "Bootstrap Testing in Nonlinear Models," G.R.E.Q.A.M. 97a39, Universite Aix-Marseille III.
  18. Jobson, J. D. & Korkie, Bob, 1982. "Potential performance and tests of portfolio efficiency," Journal of Financial Economics, Elsevier, vol. 10(4), pages 433-466, December.
  19. 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.
  20. Dufour, J.M. & Kiviet, J.F., 1995. "Exact Tests in Single Equation Autoregressive Distributed Lag Models," Cahiers de recherche 9549, Universite de Montreal, Departement de sciences economiques.
  21. Jean-Marie Dufour, 1997. "Some Impossibility Theorems in Econometrics with Applications to Structural and Dynamic Models," Econometrica, Econometric Society, vol. 65(6), pages 1365-1388, November.
  22. Rothernberg, Thomas J, 1984. "Hypothesis Testing in Linear Models When the Error Covariance Matrix Is Nonscalar," Econometrica, Econometric Society, vol. 52(4), pages 827-42, July.
  23. Breusch, T S, 1979. "Conflict among Criteria for Testing Hypotheses: Extensions and Comments," Econometrica, Econometric Society, vol. 47(1), pages 203-07, January.
  24. Davidson, R. & Mackinnon, J.G., 1996. "The Size Distorsion of Bootstrap Tests," G.R.E.Q.A.M. 96a15, Universite Aix-Marseille III.
  25. Rilstone, Paul & Veall, Michael, 1996. "Using Bootstrapped Confidence Intervals for Improved Inferences with Seemingly Unrelated Regression Equations," Econometric Theory, Cambridge University Press, vol. 12(03), pages 569-580, August.
  26. Rayner, Robert K., 1990. "Bartlett's correction and the bootstrap in normal linear regression models," Economics Letters, Elsevier, vol. 33(3), pages 255-258, July.
  27. Hashimoto, Noriko & Ohtani, Kazuhiro, 1990. "An exact test for linear restrictions in seemingly unrelated regressions with the same regressors," Economics Letters, Elsevier, vol. 32(3), pages 243-246, March.
  28. Italianer, Alexander, 1985. "A small-sample correction for the likelihood ratio test," Economics Letters, Elsevier, vol. 19(4), pages 315-317.
  29. Amsler, Christine E. & Schmidt, Peter, 1985. "A Monte Carlo investigation of the accuracy of multivariate CAPM tests," Journal of Financial Economics, Elsevier, vol. 14(3), pages 359-375, September.
  30. DUFOUR, Jean-Marie & KHALAF, Lynda, 1998. "Simulation-Based Finite-and Large-sample Inference Methods in Multivariate Regressions and Seemingly Unrelated Regressions," Cahiers de recherche 9813, Universite de Montreal, Departement de sciences economiques.
  31. Eakin, B Kelly & McMillen, Daniel P & Buono, Mark J, 1990. "Constructing Confidence Intervals Using the Bootstrap: An Application to a Multi-Product Cost Function," The Review of Economics and Statistics, MIT Press, vol. 72(2), pages 339-44, May.
  32. Stewart, Kenneth G., 1995. "The functional equivalence of the W, LR, and LM statistics," Economics Letters, Elsevier, vol. 49(2), pages 109-112, August.
  33. Bera, A. K. & Byron, R. P. & Jarque, C. M., 1981. "Further evidence on asymptotic tests for homogeneity and symmetry in large demand systems," Economics Letters, Elsevier, vol. 8(2), pages 101-105.
  34. Breusch, Trevor S., 1980. "Useful invariance results for generalized regression models," Journal of Econometrics, Elsevier, vol. 13(3), pages 327-340, August.
  35. Jayatissa, W A, 1977. "Tests of Equality between Sets of Coefficients in Two Linear Regressions when Disturbance Variances Are Unequal," Econometrica, Econometric Society, vol. 45(5), pages 1291-92, July.
  36. Shanken, Jay, 1986. " Testing Portfolio Efficiency When the Zero-Beta Rate Is Unknown: A Note," Journal of Finance, American Finance Association, vol. 41(1), pages 269-76, March.
  37. 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.
  38. Kenneth Stewart, 1997. "Exact testing in multivariate regression," Econometric Reviews, Taylor & Francis Journals, vol. 16(3), pages 321-352.
Full references (including those not matched with items on IDEAS)

Citations

Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
as in new window

Cited by:
This item has more than 25 citations. To prevent cluttering this page, these citations are listed on a separate page.

Lists

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

Statistics

Access and download statistics

Corrections

When requesting a correction, please mention this item's handle: RePEc:cir:cirwor:2000s-15. 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: (Webmaster).

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.