Robust covariance and precision matrix estimators. Based on the review of P.-L. Loh and X. L. Tan. (2018)

To install:

There are in total 4 robust covariance and 3 correlation estimation implemented, namely:

`corSpearman`

: Spearman correlation`corKendall`

: Kendall’s tau`corQuadrant`

: Quadrant correlation coefficients`covGKmat`

: Gnanadesikan-Kettenring estimator by Tarr et al. (2015) and Oellerer and Croux (2015)`covSpearmanU`

: SpearmanU covariance estimator by P.-L. Loh and X. L. Tan. (2018), The pairwise covariance matrix estimator proposed in Oellerer and Croux (2015), where the MAD estimator is combined with Spearman’s rho`covOGK`

: Orthogonalized Gnanadesikan-Kettenring (OGK) estimator by Maronna, R. A. and Zamar, R. H. (2002)`covNPD`

: Nearest Positive (semi)-Definite projection of the pairwise covariance matrix estimator considered in Tarr et al. (2015).

P.-L. Loh and X. L. Tan. (2018) then used these robust estimates in Graphical Lasso (package `glasso`

) or Quadratic Approximation (package `QUIC`

) to obtain sparse solutions to precision matrix

With `glasso`

, a function `robglasso`

stand for robust graphical LASSO is implemented. It has build in cross validation described in P.-L. Loh and X. L. Tan. (2018), for instance, to use the method with cross validation:

Where `data`

should be a matrix and `covest`

should be a function that estimate the covariance e.g. anyone mentioned above. The result list contains everything from `glasso`

output with the optimal tuning parameter found by cross validation. One can also decide fold by setting `fold`

in `robglasso`

. For more details see `?robglasso`

.