Publication Type
Journal Article
Version
acceptedVersion
Publication Date
1-2018
Abstract
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.
Keywords
Matrix equality, Trace, Determinant, Arithmetic mean, Geometric mean, Harmonic mean, Sandwich covariance matrix, Eigenvalues
Discipline
Econometrics
Research Areas
Econometrics
Publication
Journal of Econometrics
Volume
202
Issue
1
First Page
45
Last Page
56
ISSN
0304-4076
Identifier
10.1016/j.jeconom.2017.05.020
Publisher
Elsevier: 24 months
Citation
CHO, Jin Seo and PHILLIPS, Peter C. B..
Pythagorean generalization of testing the equality of two symmetric positive definite matrices. (2018). Journal of Econometrics. 202, (1), 45-56.
Available at: https://ink.library.smu.edu.sg/soe_research/2368
Copyright Owner and License
Authors
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.
Additional URL
https://doi.org/10.1016/j.jeconom.2017.05.020