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Testing the Equality of Two Positive-Definite Matrices with Application to Information Matrix Testing☆A glossary of notation and the program codes written in GAUSS for our simulations are available at:http://web.yonsei.ac.kr/jinseocho/research.htm

In: Essays in Honor of Peter C. B. Phillips

Author

Listed:
  • Jin Seo Cho
  • Halbert White

Abstract

We provide a new characterization of the equality of two positive-definite matricesAandB, 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☆A glossary of notation and the program codes written in GAUSS for our simulations are available at," Advances in Econometrics, in: Essays in Honor of Peter C. B. Phillips, volume 33, pages 491-556, Emerald Group Publishing Limited.
    • Handle: RePEc:eme:aecozz:s0731-905320140000033014
    DOI: 10.1108/S0731-905320140000033014
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    More about this item

    Keywords

    Matrix equality; information matrix test; eigenvalues; trace; determinant; C01; C12; C52;
    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

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