Estimation of the Kronecker Covariance Model by Partial Means and Quadratic Form
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We propose two new estimators of the Kronecker product model of the covariance matrix. We show that these estimators have good properties in the large dimensional case where n is large relative to T. In particular, the partial means estimator is consistent in a relative Frobenius norm sense provided ^3n/T→0, while the quadratic form estimator is consistent in a relative Frobenius norm sense provided ^3n/(nT)→0. We obtain the limiting distribution of a Lagrange multiplier (LM) test of the hypothesis of zero mean vector. We show that this test performs well in finite sample situations both when the Kronecker product model is true, but also in some cases where it is not true.
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