fsopt

hd.fsopt(S, sigma)

The infeasible finite sample optimal rotation equivariant covariance matrix estimator of Ledoit and Wolf (2018).

Parameters

Snumpy.ndarray

The sample covariance matrix.

sigmanumpy.ndarray

The (true) population covariance matrix.

Returns

outnumpy.ndarray

The finite sample optimal rotation equivariant covariance matrix estimate.

Notes

This estimator is given by

\[S_{n}^{*}:=\sum_{i=1}^{p} d_{n, i}^{*} \cdot u_{n, i} u_{n, i}^{\prime} =\sum_{i=1}^{p}\left(u_{n, i}^{\prime} \Sigma_{n} u_{n, i}\right) \cdot u_{n, i} u_{n, i}^{\prime},\]

where \(\left[u_{n, 1} \ldots u_{n, p}\right]\) are the sample eigenvectors.

References

Ledoit, O. and Wolf, M. (2018). Analytical nonlinear shrinkage of large-dimensional covariance matrices, University of Zurich, Department of Economics, Working Paper (264).