shrinkage¶

Linear shrinkage estimators for covariance matrices, following Ledoit and Wolf. Nonlinear shrinkage is planned but not yet implemented.

Sample covariance matrices are noisy when the number of variables is large relative to the number of observations. Shrinkage pulls the sample estimate toward a structured target, trading a little bias for a large reduction in variance and producing a better-conditioned, invertible estimate.

Installation¶

```bash +RHIZA_SKIP pip install git+https://github.com/Jebel-Quant/shrinkage.git

## Usage

`cov1para` implements the Ledoit-Wolf (2003) one-parameter estimator, which
shrinks the sample covariance toward a scaled identity (equal variances, zero
covariances). Pass a raw data matrix of shape `(N, p)` — `N` observations on
`p` variables:

```python
import numpy as np

from shrinkage.linear import cov1para

rng = np.random.default_rng(0)
Y = rng.standard_normal((250, 3))  # 250 observations, 3 variables

estimator = cov1para(Y)
print(estimator.shape)
print(np.allclose(estimator, estimator.T))  # symmetric

(3, 3)
True

By default the data is demeaned and the effective sample size is reduced by one. Use k=0 to skip demeaning, or k=1 if Y is already demeaned.

Documentation¶

See the API reference for the full estimator documentation.