Improved Large Covariance Matrix Estimation Based on Efficient Convex Combination and Its Application in Portfolio Optimization

Abstract

The estimation of the covariance matrix is an important topic in the field of multivariate statistical analysis. In this paper, we propose a new estimator, which is a convex combination of the linear shrinkage estimation and the rotation-invariant estimator under the Frobenius norm. We first obtain the optimal parameters by using grid search and cross-validation, and then, we use these optimal parameters to demonstrate the effectiveness and robustness of the proposed estimation in the numerical simulations. Finally, in empirical research, we apply the covariance matrix estimation to the portfolio optimization. Compared to the existing estimators, we show that the proposed estimator has better performance and lower out-of-sample risk in portfolio optimization.