Linear Shrinkage Estimation of Large Covariance Matrices with Use of Factor Models

The problem of estimating large covariance matrices with use of factor models is addressed when both the sample size and the dimension of covariance matrix tend to innity. In this paper, we consider a general class of weighted estimators which includes (i) linear combinations of the sample covariance matrix and the model-based estimator under the factor model and (ii) ridge-type estimators without factors as special cases. The optimal weights in the class are derived, and the plug-in weighted estimators are suggested since the optimal weights depend on unknown parameters. Numerical results show our methods perform well. Finally, an application to portfolio managements is given. --

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