Description Usage Arguments Details Value References

For a sample matrix, `x`

, we compute the sample covariance matrix as the
maximum likelihood estimator (MLE) of the population covariance matrix and
shrink it towards its diagonal.

1 | ```
cov_shrink_diag(x, gamma = 1)
``` |

`x` |
data matrix with |

`gamma` |
the shrinkage parameter. Must be between 0 and 1, inclusively. By default, the shrinkage parameter is 1, which simply yields the MLE. |

Let *\widehat{Σ}* be the MLE of the covariance matrix *Σ*.
Then, we shrink the MLE towards its diagonal by computing

*\widehat{Σ}(γ) = γ \widehat{Σ} + (1 - γ)
\widehat{Σ} \circ I_p,*

where *\circ* denotes the Hadamard product
and *γ \in [0,1]*.

For *γ < 1*, the resulting shrunken covariance matrix estimator is
positive definite, and for *γ = 1*, we simply have the MLE, which can
potentially be positive semidefinite (singular).

The estimator given here is based on Section 18.3.1 of the Hastie et al. (2008) text.

shrunken sample covariance matrix of size *p \times p*

Hastie, T., Tibshirani, R., and Friedman, J. (2008), "The Elements of Statistical Learning: Data Mining, Inference, and Prediction," 2nd edition. http://web.stanford.edu/~hastie/ElemStatLearn/

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