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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

Essays in Honor of Peter C. B. Phillips

ISBN: 978-1-78441-183-1

ISSN: 0731-9053

Publication date: 21 November 2014

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.

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Acknowledgements

Acknowledgments

The second author (Halbert White) had passed away before the final version was completed. The first author would like to acknowledge his contributions to this paper. He formed the outlines of the current paper. In addition, the authors are most grateful to the co-editors, Yoosoon Chang, Tom Fomby, and Joon Y. Park, and one anonymous referee. We also acknowledge helpful discussions with Anil Bera, Stephane Bonhomme, Richard Golden, Steven Henley, Atsushi Inoue, Jinook Jeong, Kiho Jeong, Michael Kashner, Hak Bae Lee, Jin Lee, Ki Young Park, Sang Soo Park, Peter C.B. Phillips, Robert Strawderman, Yoon Jae Whang, Byoungsam Yoo, Victoria Zinde-Walsh, and other participants at the 14th Advances in Econometrics Conference in Honor of Peter C.B. Phillips (Southern Methodist University, 2013), the Economics Joint Conference 2012, and the 17th Joint Workshop of Yonsei University, Hokkaido University (Hokkaido University, 2012), and KEA International Conference (Korea University, 2012). Also, Taeyoun Kim and Myungkoo Song provided excellent research assistance for our Monte Carlo experiments.

Citation

Cho, J.S. and White, H. (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: http://web.yonsei.ac.kr/jinseocho/research.htm

", Essays in Honor of Peter C. B. Phillips (Advances in Econometrics, Vol. 33), Emerald Group Publishing Limited, Bingley, pp. 491-556. https://doi.org/10.1108/S0731-905320140000033014

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Emerald Group Publishing Limited

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