Estimation of the Kronecker Covariance Model by Quadratic Form

Understand

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 Lagrange multiplier (LM) and Wald tests under both the null and local alternatives concerning the mean vector $\mu$.