ESTIMATION OF THE KRONECKER COVARIANCE MODEL BY QUADRATIC FORM

Oliver Linton and Haihan Tang

Econometric Theory, 2022, vol. 38, issue 5, 1014-1067

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 ${\log }^3n/T\to 0$ . We obtain the limiting distributions of the Lagrange multiplier and Wald tests under both the null and local alternatives concerning the mean vector $\mu $ . Testing linear restrictions of $\mu $ is also investigated. Finally, our methodology is shown to perform well in finite sample situations both when the Kronecker product model is true and when it is not true.

Date: 2022
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Working Paper: Estimation of the Kronecker Covariance Model by Quadratic Form (2020)
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