`cvCovEst`

Cross-Validated Covariance Matrix Estimation

**Authors:** Philippe Boileau, Brian Collica, and Nima Hejazi

`cvCovEst`

?`cvCovEst`

implements an efficient cross-validated procedure for covariance matrix estimation, particularly useful in high-dimensional settings. The general methodology allows for cross-validation to be used to data adaptively identify the optimal estimator of the covariance matrix from a prespecified set of candidate estimators. An overview of the framework is provided in the package vignette. For a more detailed description, see Boileau et al. (2021). A suite of plotting and diagnostic tools are also included.

For standard use, install `cvCovEst`

from CRAN:

The *development version* of the package may be installed from GitHub using `remotes`

:

To illustrate how `cvCovEst`

may be used to select an optimal covariance matrix estimator via cross-validation, consider the following toy example:

```
library(MASS)
library(cvCovEst)
set.seed(1584)
# generate a 50x50 covariance matrix with unit variances and off-diagonal
# elements equal to 0.5
Sigma <- matrix(0.5, nrow = 50, ncol = 50) + diag(0.5, nrow = 50)
# sample 50 observations from multivariate normal with mean = 0, var = Sigma
dat <- mvrnorm(n = 50, mu = rep(0, 50), Sigma = Sigma)
# run CV-selector
cv_cov_est_out <- cvCovEst(
dat = dat,
estimators = c(linearShrinkLWEst, denseLinearShrinkEst,
thresholdingEst, poetEst, sampleCovEst),
estimator_params = list(
thresholdingEst = list(gamma = c(0.2, 2)),
poetEst = list(lambda = c(0.1, 0.2), k = c(1L, 2L))
),
cv_loss = cvMatrixFrobeniusLoss,
cv_scheme = "v_fold",
v_folds = 5
)
# print the table of risk estimates
# NOTE: the estimated covariance matrix is accessible via the `$estimate` slot
cv_cov_est_out$risk_df
#> # A tibble: 9 × 3
#> estimator hyperparameters cv_risk
#> <chr> <chr> <dbl>
#> 1 linearShrinkLWEst hyperparameters = NA 357.
#> 2 poetEst lambda = 0.2, k = 1 369.
#> 3 poetEst lambda = 0.2, k = 2 372.
#> 4 poetEst lambda = 0.1, k = 2 375.
#> 5 poetEst lambda = 0.1, k = 1 376.
#> 6 denseLinearShrinkEst hyperparameters = NA 379.
#> 7 sampleCovEst hyperparameters = NA 379.
#> 8 thresholdingEst gamma = 0.2 384.
#> 9 thresholdingEst gamma = 2 826.
```

If you encounter any bugs or have any specific feature requests, please file an issue.

Contributions are very welcome. Interested contributors should consult our contribution guidelines prior to submitting a pull request.

Please cite the following paper when using the `cvCovEst`

R software package.

```
@article{cvCovEst2021,
doi = {10.21105/joss.03273},
url = {https://doi.org/10.21105/joss.03273},
year = {2021},
publisher = {The Open Journal},
volume = {6},
number = {63},
pages = {3273},
author = {Philippe Boileau and Nima S. Hejazi and Brian Collica and Mark J. van der Laan and Sandrine Dudoit},
title = {cvCovEst: Cross-validated covariance matrix estimator selection and evaluation in `R`},
journal = {Journal of Open Source Software}
}
```

When describing or discussing the theory underlying the `cvCovEst`

method, or simply using the method, please cite the pre-print below.

```
@article{boileau2022,
author = {Philippe Boileau and Nima S. Hejazi and Mark J. van der Laan and Sandrine Dudoit},
doi = {10.1080/10618600.2022.2110883},
eprint = {https://doi.org/10.1080/10618600.2022.2110883},
journal = {Journal of Computational and Graphical Statistics},
number = {ja},
pages = {1-28},
publisher = {Taylor & Francis},
title = {Cross-Validated Loss-Based Covariance Matrix Estimator Selection in High Dimensions},
url = {https://doi.org/10.1080/10618600.2022.2110883},
volume = {0},
year = {2022},
bdsk-url-1 = {https://doi.org/10.1080/10618600.2022.2110883}}
```

© 2020-2023 Philippe Boileau

The contents of this repository are distributed under the MIT license. See file `LICENSE.md`

for details.

Boileau, Philippe, Nima S. Hejazi, Mark J. van der Laan, and Sandrine Dudoit. 2021. “Cross-Validated Loss-Based Covariance Matrix Estimator Selection in High Dimensions.” https://arxiv.org/abs/2102.09715.