Table 1 Notation Definitions.
From: Application of regularized covariance matrices in logistic regression and portfolio optimization
Notation | Definition |
|---|---|
\(\Sigma ^*\) | True covariance matrix, \(\Sigma ^* \in \mathbb {R}^{p \times p}\) |
\(\hat{\Sigma }_{\text {emp}}\) | Sample covariance matrix, \(\hat{\Sigma }_{\text {emp}} = \frac{1}{n} \sum _{i=1}^n (X_i - \bar{X})(X_i - \bar{X})^T\) |
\(\hat{\Sigma }_\lambda\) | Regularized covariance matrix, \(\hat{\Sigma }_\lambda = \hat{\Sigma }_{\text {emp}} + \lambda I\) |
\(|| \cdot ||_F\) | Frobenius norm |
\(\text {Tr}(\cdot )\) | Trace operator |
\(\otimes\) | Kronecker product |
p | Dimensionality of the covariance matrix |
n | Number of samples |
\(\lambda\) | Regularization parameter |
