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We propose a Kronecker product model for correlation or covariance matricesin the large dimensional case. The number of parameters of the model increaseslogarithmically with the dimension of the matrix. We propose a minimum distance(MD) estimator based on a log-linear property of the model, as well as aone-step estimator, which is a one-step approximation to the quasi-maximumlikelihood estimator (QMLE). We establish rates of convergence and centrallimit theorems (CLT) for our estimators in the large dimensional case. Aspecification test and tools for Kronecker product model selection andinference are provided. In a Monte Carlo study where a Kronecker product modelis correctly specified, our estimators exhibit superior performance. In anempirical application to portfolio choice for SP500 daily returns, wedemonstrate that certain Kronecker product models are good approximations tothe general covariance matrix.

Estimation of a Multiplicative Correlation Structure in the Large Dimensional Case