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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Main Authors: CHO, Jin Seo, PHILLIPS, Peter C. B.
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Language:English
Published: Institutional Knowledge at Singapore Management University 2018
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Online Access: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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spelling 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
institution Singapore Management University
building SMU Libraries
continent Asia
country Singapore
Singapore
content_provider SMU Libraries
collection InK@SMU
language English
topic Matrix equality
Trace
Determinant
Arithmetic mean
Geometric mean
Harmonic mean
Sandwich covariance matrix
Eigenvalues
Econometrics
spellingShingle 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
description 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.
format text
author CHO, Jin Seo
PHILLIPS, Peter C. B.
author_facet CHO, Jin Seo
PHILLIPS, Peter C. B.
author_sort 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
publisher Institutional Knowledge at Singapore Management University
publishDate 2018
url 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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