skfolio.metrics.exceedance_rate#
- skfolio.metrics.exceedance_rate(squared_distances, n_features, confidence_level)[source]#
Exceedance rate for chi-squared calibration statistics.
Computes the fraction of squared distances exceeding the upper
confidence_levelchi-squared quantile.The reference threshold assumes Gaussian standardized returns. In practice, the rate is sensitive not only to covariance misspecification but also to heavy tails, regime shifts, and non-Gaussian standardized returns. It is best used as a comparative metric across estimators rather than as an absolute calibration test.
- Parameters:
- squared_distancesarray-like of shape (n_observations,)
Squared Mahalanobis distances or similar chi-squared statistics.
- n_featuresint
Degrees of freedom (number of features/assets).
- confidence_levelfloat
Coverage confidence level used to define the upper chi-squared threshold. For example,
0.95corresponds to an expected exceedance rate of0.05under calibration.
- Returns:
- float
Observed exceedance rate. It should be close to \(1 - \text{confidence\_level}\) when the reference chi-squared approximation is appropriate.
See also
mahalanobis_calibration_ratioCalibration ratio based on squared Mahalanobis distances.
Notes
Under correct calibration and Gaussian standardized returns, \(d^2 \sim \chi^2(n_{\text{features}})\), so \(P(d^2 > \chi^2_{\text{confidence\_level}}) = 1 - \text{confidence\_level}\).