How to install

The development version from GitHub:

# install.packages("remotes")
remotes::install_github("AlexisDerumigny/UniversalShrink")

1. Functions for estimation of the covariance matrix

• cov_analytical_NL_shrinkage() and cov_quadratic_inverse_shrinkage(): perform estimation of the covariance matrix using non-linear shrinkage. Both estimators are optimal for the Frobenius norm (asymptotically).

2. Functions for estimation of the precision matrix

2.1. Moore-Penrose-type estimators

• Moore_Penrose(): Moore-Penrose estimator of the precision matrix, obtained by computing the Moore-Penrose inverse of the sample covariance matrix.

• Moore_Penrose_target(): perform a first-order shrinkage of the Moore-Penrose estimator of the precision matrix, towards an arbitrary (fixed) target such as the identity matrix.

• Moore_Penrose_higher_order_shrinkage(): estimate the precision matrix via a polynomial in the Moore-Penrose estimator of the precision matrix.

2.2. Ridge-type estimators

• ridge_no_shrinkage(): the usual ridge estimator

• ridge_target(): perform first-order shrinkage of the Ridge estimator towards an arbitrary (fixed) target such as the identity matrix.

• ridge_higher_order_shrinkage(): perform higher-order shrinkage of the Ridge estimator

• ridge_shrinkage_rescaled()

2.3. Moore-Penrose-Ridge "hybrid" estimators

• MPR_no_shrinkage()

• MPR_target()

3. Functions for estimation of optimal portfolio weights

• From a given precision matrix, one can get the optimal portfolio weights (GMV for Global Minimum Variance) using the function GMV_PlugIn(). This can also be used by giving as input an estimator of the precision matrix, which then will give as output an estimator of the optimal portfolio weights.

• GMV_Moore_Penrose(): using the Moore-Penrose inverse Moore_Penrose() of the precision matrix as an input for the plug-in estimation.

• GMV_Moore_Penrose_target(): performs a first-order shrinkage of the estimator given by GMV_Moore_Penrose() towards an arbitrary (fixed) portfolio such as the equally weighted portfolio.