Linton, O. and Tang, H.

Estimation of the Kronecker Covariance Model by Quadratic Form

Econometric Theory, forthcoming

pp. 1-54 (2021)

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

Publisher's Link: https://doi.org/10.1017/S026646662000050X