Estimation of the Kronecker Covariance Model by Quadratic Form

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 ${\log }^{3}n/T\to 0$. We obtain the limiting distributions of Lagrange multiplier (LM) and Wald tests under both the null and local alternatives concerning the mean vector $\mu$. Testing linear restrictions of $\mu$ 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.

References in corpus (5)

• Covariance regularization by thresholding
• Nonlinear shrinkage estimation of large-dimensional covariance matrices
• High-dimensional covariance matrix estimation in approximate factor models
• Multilinear tensor regression for longitudinal relational data
• Inference without smoothing for large panels with cross-sectional and temporal dependence

Cited by in corpus (1)

• Rank Determination in Tensor Factor Model