IDEAS home Printed from https://ideas.repec.org/a/ecm/emetrp/v54y1986i4p881-95.html
   My bibliography  Save this article

The Exact Distribution of the Wald Statistic

Author

Listed:
  • Phillips, P C B

Abstract

This paper derives the exact distribution of the Wald statistic for testing general linear restrictions on the coefficients in the multivariate linear model. This generalizes all previously known results including those for the standard F statistic in linear regression, for Hotelling's T^{2} test and for Hotelling's generalized T_{0}^{2} test. Conventional classical assumptions of normally distributed errors and nonrandom exogenous variables are employed.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Phillips, P C B, 1986. "The Exact Distribution of the Wald Statistic," Econometrica, Econometric Society, vol. 54(4), pages 881-895, July.
    • Handle: RePEc:ecm:emetrp:v:54:y:1986:i:4:p:881-95
    as

    Download full text from publisher

    File URL: http://links.jstor.org/sici?sici=0012-9682%28198607%2954%3A4%3C881%3ATEDOTW%3E2.0.CO%3B2-W&origin=repec
    File Function: full text
    Download Restriction: Access to full text is restricted to JSTOR subscribers. See http://www.jstor.org for details.
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Phillips, P.C.B., 1984. "The exact distribution of the Stein-rule estimator," Journal of Econometrics, Elsevier, vol. 25(1-2), pages 123-131.
    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


    Cited by:

    1. Yong Bao & Xiaotian Liu & Aman Ullah, 2020. "On the Exact Statistical Distribution of Econometric Estimators and Test Statistics," Working Papers 202014, University of California at Riverside, Department of Economics, revised Jun 2020.
    2. Attfield, C. L. F., 1997. "Estimating a cointegrating demand system," European Economic Review, Elsevier, vol. 41(1), pages 61-73, January.
    3. Phillips, Peter C B, 1994. "Some Exact Distribution Theory for Maximum Likelihood Estimators of Cointegrating Coefficients in Error Correction Models," Econometrica, Econometric Society, vol. 62(1), pages 73-93, January.
    4. Peter C.B. Phillips, 1985. "Fractional Matrix Calculus and the Distribution of Multivariate Tests," Cowles Foundation Discussion Papers 767, Cowles Foundation for Research in Economics, Yale University.
    5. Grant Hillier & Raymond Kan & Xiaolu Wang, 2008. "Generating functions and short recursions, with applications to the moments of quadratic forms in noncentral normal vectors," CeMMAP working papers CWP14/08, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    6. Hillier, Grant & Kan, Raymond & Wang, Xiaolu, 2009. "Computationally Efficient Recursions For Top-Order Invariant Polynomials With Applications," Econometric Theory, Cambridge University Press, vol. 25(1), pages 211-242, February.
    7. Peter C. B. Phillips, 2021. "Pitfalls in Bootstrapping Spurious Regression," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 19(1), pages 163-217, December.
    8. Neil R. Ericsson, 1987. "Monte Carlo methodology and the finite sample properties of statistics for testing nested and non-nested hypotheses," International Finance Discussion Papers 317, Board of Governors of the Federal Reserve System (U.S.).
    9. Giovanni Forchini, "undated". "The Distribution of a Ratio of Quadratic Forms in Noncentral Normal Variables," Discussion Papers 01/12, Department of Economics, University of York.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Peter C.B. Phillips, 1990. "Operational Algebra and Regression t-Tests," Cowles Foundation Discussion Papers 948, Cowles Foundation for Research in Economics, Yale University.
    2. Peter C. B. Phillips, 2021. "Pitfalls in Bootstrapping Spurious Regression," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 19(1), pages 163-217, December.
    3. Akio Namba, 2021. "Bootstrapping the Stein-Rule Estimators," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 19(1), pages 219-237, December.
    4. Zhang, Xinyu & Chen, Ti & Wan, Alan T.K. & Zou, Guohua, 2009. "Robustness of Stein-type estimators under a non-scalar error covariance structure," Journal of Multivariate Analysis, Elsevier, vol. 100(10), pages 2376-2388, November.
    5. Peter C.B. Phillips, 1983. "The Exact Distribution of Zellner's SUR," Cowles Foundation Discussion Papers 680, Cowles Foundation for Research in Economics, Yale University.
    6. Ohtani, Kazuhiro & Kozumi, Hideo, 1996. "The exact general formulae for the moments and the MSE dominance of the Stein-rule and positive-part Stein-rule estimators," Journal of Econometrics, Elsevier, vol. 74(2), pages 273-287, October.
    7. Peter C.B. Phillips, 1985. "Fractional Matrix Calculus and the Distribution of Multivariate Tests," Cowles Foundation Discussion Papers 767, Cowles Foundation for Research in Economics, Yale University.
    8. Li, Haiqi & Chen, Xingyi & Liang, Jufang, 2022. "Shrinkage estimation of panel data models with interactive effects," Economics Letters, Elsevier, vol. 210(C).

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:ecm:emetrp:v:54:y:1986:i:4:p:881-95. See general information about how to correct material in RePEc.

    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 CitEc recognized a bibliographic reference but did not link an item in RePEc 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 RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: https://edirc.repec.org/data/essssea.html .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.