prial¶
-
loss.prial(S_list, sigma_hat_list, sigma, loss_func=None)[source]¶ The percentage relative improvement in average loss (PRIAL) over the sample covariance matrix.
- Parameters
- S_listlist of numpy.ndarray
The sample covariance matrix.
- sigma_hat_listlist of numpy.ndarray
The covariance matrix estimate using the estimator of interest.
- sigmanumpy.ndarray
The (true) population covariance matrix.
- loss_funcfunction, defualt = None
The loss function. If
Nonethe minimum variance loss function is used.
- Returns
- prialfloat
The PRIAL.
Notes
The percentage relative improvement in average loss (PRIL) over the sample covariance matrix is given by:
\[\mathrm{PRIAL}_{n}\left(\widehat{\Sigma}_{n}\right):= \frac{\mathbb{E}\left[\mathcal{L}_{n}\left(S_{n}, \Sigma_{n}\right)\right]-\mathbb{E}\left[\mathcal{L}_{n} \left(\widehat{\Sigma}_{n}, \Sigma_{n}\right)\right]} {\mathbb{E}\left[\mathcal{L}_{n}\left(S_{n}, \Sigma_{n}\right)\right]-\mathbb{E}\left[\mathcal{L}_{n} \left(S_{n}^{*}, \Sigma_{n}\right)\right]} \times 100 \%\]
