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Pythagorean generalization of testing the equality of two symmetric positive definite matrices

Pythagorean generalization of testing the equality of two symmetric positive definite matrices
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 between two dimensional symmetric positive-definite matrices and : the traces of and are equal to if and only if . 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.
0304-4076
Cho, Jin Seo
73c54d86-de50-44c7-8d1f-afbfab67bfc1
Phillips, Peter C.B.
f67573a4-fc30-484c-ad74-4bbc797d7243
Cho, Jin Seo
73c54d86-de50-44c7-8d1f-afbfab67bfc1
Phillips, Peter C.B.
f67573a4-fc30-484c-ad74-4bbc797d7243

Cho, Jin Seo and Phillips, Peter C.B. (2017) Pythagorean generalization of testing the equality of two symmetric positive definite matrices. Journal of Econometrics. (doi:10.1016/j.jeconom.2017.05.020).

Record type: Article

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 dimensional symmetric positive-definite matrices and : the traces of and are equal to if and only if . 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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JSCHO_05-09-17_IMTest - Accepted Manuscript
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More information

Accepted/In Press date: 10 May 2017
e-pub ahead of print date: 5 October 2017

Identifiers

Local EPrints ID: 414963
URI: https://eprints.soton.ac.uk/id/eprint/414963
ISSN: 0304-4076
PURE UUID: 89c14bfd-ccc4-4c2c-8789-fc979c334f22
ORCID for Peter C.B. Phillips: ORCID iD orcid.org/0000-0003-2341-0451

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Date deposited: 18 Oct 2017 16:30
Last modified: 20 Jul 2019 00:47

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