Linton, O. and Tang, H.
Estimation of the Kronecker Covariance Model by Quadratic Form
CWPE2050
Abstract: We propose a new estimator, the quadratic form estimator, of the Kronecker product model for covariance matrices. We show that this estimator has good properties in the large dimensional case (i.e., the cross-sectional dimension n is large relative to the sample size T). In particular, the quadratic form estimator is consistent in a relative Frobenius norm sense provided log3 n/T→ 0. We obtain the limiting distributions of Lagrange multiplier (LM) and Wald tests under both the null and local alternatives concerning the mean vector μ. Testing linear restrictions of μ is also investigated. Finally, our methodology performs well in the finite-sample situations both when the Kronecker product model is true, and when it is not true.
Keywords: Covariance matrix, Kronecker product, Quadratic form, Lagrange multiplier test, Wald test
Author links: Oliver Linton
PDF: https://www.econ.cam.ac.uk/research-files/repec/cam/pdf/cwpe2050.pdf 
Open Access Link: https://doi.org/10.17863/CAM.61827
Published Version of Paper: Estimation of the Kronecker Covariance Model by Quadratic Form, Linton, O. and Tang, H., Econometric Theory, forthcoming (2021)
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