IDEAS home Printed from https://ideas.repec.org/p/yon/wpaper/2014rwp-67.html
   My bibliography  Save this paper

Testing the Equality of Two Positive-Definite Matrices with Application to Information Matrix Testing

Author

Listed:
  • JIN SEO CHO

    (Yonsei University)

  • HALBERT WHITE

    (University of California, San Diego)

Abstract

We provide a new characterization of the equality of two positive-definite matrices A and B, and we use this to propose several new computationally convenient statistical tests for the equality of two unknown positive-definite matrices. Our primary focus is on testing the information matrix equality (e.g., White, 1982, 1994). We characterize the asymptotic behavior of our new trace-determinant information matrix test statistics under the null and the alternative and investigate their finite-sample performance for a variety of models: linear regression, exponential duration, probit, and Tobit. The parametric bootstrap suggested by Horowitz (1994) delivers critical values that provide admirable level behavior, even in samples as small as n ¨¡ 50. Our new tests often have better power than the parametric-bootstrap version of the traditional IMT; when they do not, they nevertheless perform respectably.

Suggested Citation

  • Jin Seo Cho & Halbert White, 2014. "Testing the Equality of Two Positive-Definite Matrices with Application to Information Matrix Testing," Working papers 2014rwp-67, Yonsei University, Yonsei Economics Research Institute.
    • Handle: RePEc:yon:wpaper:2014rwp-67
    as

    Download full text from publisher

    File URL: http://121.254.254.220/repec/yon/wpaper/2014rwp-67.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Nagarsenker, B. N. & Pillai, K. C. S., 1973. "The distribution of the sphericity test criterion," Journal of Multivariate Analysis, Elsevier, vol. 3(2), pages 226-235, June.
    2. White,Halbert, 1996. "Estimation, Inference and Specification Analysis," Cambridge Books, Cambridge University Press, number 9780521574464.
    3. Abadir,Karim M. & Magnus,Jan R., 2005. "Matrix Algebra," Cambridge Books, Cambridge University Press, number 9780521537469.
    4. Cho, Jin Seo & White, Halbert, 2010. "Testing for unobserved heterogeneity in exponential and Weibull duration models," Journal of Econometrics, Elsevier, vol. 157(2), pages 458-480, August.
    5. Vaart,A. W. van der, 2000. "Asymptotic Statistics," Cambridge Books, Cambridge University Press, number 9780521784504.
    6. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
    7. Pillai, K. C. S. & Nagarsenker, B. N., 1972. "On the distributions of a class of statistics in multivariate analysis," Journal of Multivariate Analysis, Elsevier, vol. 2(1), pages 96-114, March.
    8. Maxwell L. King & Xibin Zhang & Muhammad Akram, 2011. "A New Procedure For Multiple Testing Of Econometric Models," Monash Econometrics and Business Statistics Working Papers 7/11, Monash University, Department of Econometrics and Business Statistics.
    9. repec:cup:cbooks:9780521822893 is not listed on IDEAS
    10. Gerard J. van den Berg & Geert Ridder, 1998. "An Empirical Equilibrium Search Model of the Labor Market," Econometrica, Econometric Society, vol. 66(5), pages 1183-1222, September.
    11. Alastair Hall, 1987. "The Information Matrix Test for the Linear Model," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 54(2), pages 257-263.
    12. Taylor, Larry W., 1987. "The size bias of White's information matrix test," Economics Letters, Elsevier, vol. 24(1), pages 63-67.
    13. Horowitz, Joel L., 1994. "Bootstrap-based critical values for the information matrix test," Journal of Econometrics, Elsevier, vol. 61(2), pages 395-411, April.
    14. Xiaohong Chen & Norman R. Swanson (ed.), 2013. "Recent Advances and Future Directions in Causality, Prediction, and Specification Analysis," Springer Books, Springer, edition 127, number 978-1-4614-1653-1, December.
    15. Jin Seo Cho & Halbert White, 2007. "Testing for Regime Switching," Econometrica, Econometric Society, vol. 75(6), pages 1671-1720, November.
    16. Strawderman, Robert L., 1994. "A note on necessary and sufficient conditions for proving that a random symmetric matrix converges to a given limit," Statistics & Probability Letters, Elsevier, vol. 21(5), pages 367-370, December.
    17. Orme, Chris, 1990. "The small-sample performance of the information-matrix test," Journal of Econometrics, Elsevier, vol. 46(3), pages 309-331, December.
    18. Lancaster, Tony, 1979. "Econometric Methods for the Duration of Unemployment," Econometrica, Econometric Society, vol. 47(4), pages 939-956, July.
    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. Cho, Jin Seo & Phillips, Peter C.B., 2018. "Pythagorean generalization of testing the equality of two symmetric positive definite matrices," Journal of Econometrics, Elsevier, vol. 202(1), pages 45-56.
    2. Lijuan Huo & Jin Seo Cho, 2021. "Testing for the sandwich-form covariance matrix of the quasi-maximum likelihood estimator," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(2), pages 293-317, June.
    3. Jin Seo Cho & Peter C.B. Phillips, 2016. "Online Supplement to "Pythagorean Generalization of Testing the Equality of Two Symmetric Positive Definite Matrices"," Working papers 2016rwp-89a, Yonsei University, Yonsei Economics Research Institute.
    4. Jin Seo Cho & Peter C. B. Phillips & Juwon Seo, 2022. "Parametric Conditional Mean Inference With Functional Data Applied To Lifetime Income Curves," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 63(1), pages 391-456, February.
    5. Richard M. Golden & Steven S. Henley & Halbert White & T. Michael Kashner, 2016. "Generalized Information Matrix Tests for Detecting Model Misspecification," Econometrics, MDPI, vol. 4(4), pages 1-24, November.
    6. Seok Young Hong & Oliver Linton & Hui Jun Zhang, 2015. "An investigation into multivariate variance ratio statistics and their application to stock market predictability," CeMMAP working papers 13/15, Institute for Fiscal Studies.
    7. Perera, Indeewara & Silvapulle, Mervyn J., 2023. "Bootstrap specification tests for dynamic conditional distribution models," Journal of Econometrics, Elsevier, vol. 235(2), pages 949-971.
    8. Seok Young Hong & Oliver Linton & Hui Jun Zhang, 2015. "An investigation into Multivariate Variance Ratio Statistics and their application to Stock Market Predictability," Cambridge Working Papers in Economics 1552, Faculty of Economics, University of Cambridge.
    9. Richard M. Golden & Steven S. Henley & Halbert White & T. Michael Kashner, 2019. "Consequences of Model Misspecification for Maximum Likelihood Estimation with Missing Data," Econometrics, MDPI, vol. 7(3), pages 1-27, September.
    10. Jin Seo Cho & Peter C.B. Phillips, "undated". "Testing Equality of Covariance Matrices via Pythagorean Means," Cowles Foundation Discussion Papers 1970, Cowles Foundation for Research in Economics, Yale University.

    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. Cho, Jin Seo & Phillips, Peter C.B., 2018. "Pythagorean generalization of testing the equality of two symmetric positive definite matrices," Journal of Econometrics, Elsevier, vol. 202(1), pages 45-56.
    2. Jin Seo Cho & Peter C.B. Phillips, "undated". "Testing Equality of Covariance Matrices via Pythagorean Means," Cowles Foundation Discussion Papers 1970, Cowles Foundation for Research in Economics, Yale University.
    3. Cho, Jin Seo & White, Halbert, 2010. "Testing for unobserved heterogeneity in exponential and Weibull duration models," Journal of Econometrics, Elsevier, vol. 157(2), pages 458-480, August.
    4. Riccardo Lucchetti & Claudia Pigini, 2013. "A test for bivariate normality with applications in microeconometric models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 22(4), pages 535-572, November.
    5. Dhaene, Geert & Hoorelbeke, Dirk, 2004. "The information matrix test with bootstrap-based covariance matrix estimation," Economics Letters, Elsevier, vol. 82(3), pages 341-347, March.
    6. Davidson, Russell & MacKinnon, James G, 1998. "Graphical Methods for Investigating the Size and Power of Hypothesis Tests," The Manchester School of Economic & Social Studies, University of Manchester, vol. 66(1), pages 1-26, January.
    7. K. Chua & S. Ong, 2013. "Test of misspecification with application to negative binomial distribution," Computational Statistics, Springer, vol. 28(3), pages 993-1009, June.
    8. George Neumann, 1996. "Search Models and Duration Data," Econometrics 9602008, University Library of Munich, Germany, revised 07 Mar 1996.
    9. Stomberg, Christopher & White, Halbert, 2000. "Bootstrapping the Information Matrix Test," University of California at San Diego, Economics Working Paper Series qt158451cr, Department of Economics, UC San Diego.
    10. Jin Seo Cho & Peter C. B. Phillips & Juwon Seo, 2019. "Parametric Inference on the Mean of Functional Data Applied to Lifetime Income Curves," Working papers 2019rwp-153, Yonsei University, Yonsei Economics Research Institute.
    11. Jin Seo Cho & Peter C. B. Phillips & Juwon Seo, 2022. "Parametric Conditional Mean Inference With Functional Data Applied To Lifetime Income Curves," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 63(1), pages 391-456, February.
    12. King, Maxwell L. & Zhang, Xibin & Akram, Muhammad, 2020. "Hypothesis testing based on a vector of statistics," Journal of Econometrics, Elsevier, vol. 219(2), pages 425-455.
    13. Jin Seo Cho & Jin Seok Park & Sang Woo Park, 2018. "Testing for the Conditional Geometric Mixture Distribution," Working papers 2018rwp-123, Yonsei University, Yonsei Economics Research Institute.
    14. repec:ebl:ecbull:v:3:y:2008:i:5:p:1-7 is not listed on IDEAS
    15. Davidson, Russell & MacKinnon, James G., 1989. "Testing for Consistency using Artificial Regressions," Econometric Theory, Cambridge University Press, vol. 5(3), pages 363-384, December.
    16. Wanling Huang & Artem Prokhorov, 2014. "A Goodness-of-fit Test for Copulas," Econometric Reviews, Taylor & Francis Journals, vol. 33(7), pages 751-771, October.
    17. Mai, Tien & Frejinger, Emma & Bastin, Fabian, 2015. "A misspecification test for logit based route choice models," Economics of Transportation, Elsevier, vol. 4(4), pages 215-226.
    18. Teresa Aparicio & Inmaculada Villanua, 2001. "The asymptotically efficient version of the information matrix test in binary choice models. A study of size and power," Journal of Applied Statistics, Taylor & Francis Journals, vol. 28(2), pages 167-182.
    19. Maxwell L. King & Xibin Zhang & Muhammad Akram, 2011. "A New Procedure For Multiple Testing Of Econometric Models," Monash Econometrics and Business Statistics Working Papers 7/11, Monash University, Department of Econometrics and Business Statistics.
    20. Samarjit Das & Nityananda Sarkar, 2010. "Is the relative risk aversion parameter constant over time? A multi-country study," Empirical Economics, Springer, vol. 38(3), pages 605-617, June.
    21. Daisuke Nagakura, 2008. "A note on the relationship between the information matrx test and a score test for parameter constancy," Economics Bulletin, AccessEcon, vol. 3(5), pages 1-7.

    More about this item

    Keywords

    Matrix equality; Information matrix test; Eigenvalues; Trace; Determinant; Eigenspectrum test; Parametric Bootstrap.;
    All these keywords.

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:yon:wpaper:2014rwp-67. 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: YERI (email available below). General contact details of provider: https://edirc.repec.org/data/eryonkr.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.