Pythagorean generalization of testing the equality of two symmetric positive definite matrices
We provide a new test for equality of two symmetric positive-definite matrices that leads to a convenient mechanism for testing specification using the information matrix equality or the sandwich asymptotic covariance matrix of the GMM estimator. The test relies on a new characterization of equality...
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sg-smu-ink.soe_research-33672020-04-09T06:39:53Z Pythagorean generalization of testing the equality of two symmetric positive definite matrices CHO, Jin Seo PHILLIPS, Peter C. B. We provide a new test for equality of two symmetric positive-definite matrices that leads to a convenient mechanism for testing specification using the information matrix equality or the sandwich asymptotic covariance matrix of the GMM estimator. The test relies on a new characterization of equality between two k dimensional symmetric positive-definite matrices A and B: the traces of AB−1 and BA−1 are equal to k if and only if A=B. Using this simple criterion, we introduce a class of omnibus test statistics for equality and examine their null and local alternative approximations under some mild regularity conditions. A preferred test in the class with good omni-directional power is recommended for practical work. Monte Carlo experiments are conducted to explore performance characteristics under the null and local as well as fixed alternatives. The test is applicable in many settings, including GMM estimation, SVAR models and high dimensional variance matrix settings. 2018-01-01T08:00:00Z text application/pdf https://ink.library.smu.edu.sg/soe_research/2368 info:doi/10.1016/j.jeconom.2017.05.020 https://ink.library.smu.edu.sg/context/soe_research/article/3367/viewcontent/JSCHO_05_09_17_IMTest_av.pdf http://creativecommons.org/licenses/by-nc-nd/4.0/ Research Collection School Of Economics eng Institutional Knowledge at Singapore Management University Matrix equality Trace Determinant Arithmetic mean Geometric mean Harmonic mean Sandwich covariance matrix Eigenvalues Econometrics |
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Matrix equality Trace Determinant Arithmetic mean Geometric mean Harmonic mean Sandwich covariance matrix Eigenvalues Econometrics CHO, Jin Seo PHILLIPS, Peter C. B. Pythagorean generalization of testing the equality of two symmetric positive definite matrices |
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We provide a new test for equality of two symmetric positive-definite matrices that leads to a convenient mechanism for testing specification using the information matrix equality or the sandwich asymptotic covariance matrix of the GMM estimator. The test relies on a new characterization of equality between two k dimensional symmetric positive-definite matrices A and B: the traces of AB−1 and BA−1 are equal to k if and only if A=B. Using this simple criterion, we introduce a class of omnibus test statistics for equality and examine their null and local alternative approximations under some mild regularity conditions. A preferred test in the class with good omni-directional power is recommended for practical work. Monte Carlo experiments are conducted to explore performance characteristics under the null and local as well as fixed alternatives. The test is applicable in many settings, including GMM estimation, SVAR models and high dimensional variance matrix settings. |
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CHO, Jin Seo PHILLIPS, Peter C. B. |
author_facet |
CHO, Jin Seo PHILLIPS, Peter C. B. |
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CHO, Jin Seo |
title |
Pythagorean generalization of testing the equality of two symmetric positive definite matrices |
title_short |
Pythagorean generalization of testing the equality of two symmetric positive definite matrices |
title_full |
Pythagorean generalization of testing the equality of two symmetric positive definite matrices |
title_fullStr |
Pythagorean generalization of testing the equality of two symmetric positive definite matrices |
title_full_unstemmed |
Pythagorean generalization of testing the equality of two symmetric positive definite matrices |
title_sort |
pythagorean generalization of testing the equality of two symmetric positive definite matrices |
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Institutional Knowledge at Singapore Management University |
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2018 |
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https://ink.library.smu.edu.sg/soe_research/2368 https://ink.library.smu.edu.sg/context/soe_research/article/3367/viewcontent/JSCHO_05_09_17_IMTest_av.pdf |
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