.. _example_covariance_plot_covariance_estimation.py: =========================================== Ledoit-Wolf vs Covariance simple estimation =========================================== The usual covariance maximum likelihood estimate can be regularized using shrinkage. Ledoit and Wolf proposed a close formula to compute the asymptotical optimal shrinkage parameter (minimizing a MSE criterion), yielding the Ledoit-Wolf covariance estimate. Chen et al. proposed an improvement of the Ledoit-Wolf shrinkage parameter, the OAS coefficient, whose convergence is significantly better under the assumption that the data are gaussian. In this example, we compute the likelihood of unseen data for different values of the shrinkage parameter, highlighting the LW and OAS estimates. The Ledoit-Wolf estimate stays close to the likelihood criterion optimal value, which is an artifact of the method since it is asymptotic and we are working with a small number of observations. The OAS estimate deviates from the likelihood criterion optimal value but better approximate the MSE optimal value, especially for a small number a observations. .. image:: images/plot_covariance_estimation_1.png :align: center **Python source code:** :download:`plot_covariance_estimation.py ` .. literalinclude:: plot_covariance_estimation.py :lines: 25-