EI Namespace

The exported unibm.ei namespace groups the persistence-side workflow: sample preparation, BM-path construction, stable-window selection, pooled BM estimators, threshold estimators, plotting helpers, and bootstrap-based covariance support.

ei

Canonical EI-facing UniBM subpackage.

EI_DEFAULT_COVARIANCE_SHRINKAGE = 0.35 module-attribute

EI_ALPHA = 0.05 module-attribute

EI_CI_LEVEL = 1.0 - EI_ALPHA module-attribute

EI_TINY = 1e-08 module-attribute

__all__ = ['EI_ALPHA', 'EI_CI_LEVEL', 'EI_DEFAULT_COVARIANCE_SHRINKAGE', 'EI_TINY', 'EiPathBundle', 'EiPreparedBundle', 'EiStableWindow', 'ExtremalIndexEstimate', 'ThresholdCandidate', 'bootstrap_bm_ei_path', 'bootstrap_bm_ei_path_draws', 'estimate_ferro_segers', 'estimate_k_gaps', 'estimate_native_bm_ei', 'estimate_pooled_bm_ei', 'extract_stable_path_window', 'plot_ei_fit', 'plot_ei_path', 'prepare_ei_bundle', 'select_stable_path_window'] module-attribute

EiPathBundle dataclass

Observed BM-EI path ingredients for one base-path and block scheme.

theta_path and z_path are computed from the observed series over the candidate block-size grid. stable_window and selected_level record where that observed path is judged stable, while sample_statistics preserves the per-block-size window statistics reused by native fixed-b estimators.

EiPreparedBundle dataclass

Reusable EI preparation outputs derived from one observed series.

The bundle stores the cleaned observed values, the candidate block-size grid, all BM path variants, and threshold-side exceedance candidates so the native BM, pooled BM, and threshold estimators can all reuse the same preparation step.

EiStableWindow dataclass

Selected stable window on an integer tuning axis.

ExtremalIndexEstimate dataclass

Unified formal-EI result container.

Most users should read theta_hat and confidence_interval first, then inspect stable_window, regression, and base_path to understand which formal estimator produced the headline result. path_level, path_theta, and path_eir are retained for path diagnostics and plotting rather than for headline reporting.

ThresholdCandidate dataclass

One threshold-side EI fit before cross-threshold selection.

bootstrap_bm_ei_path(vec, *, base_path, sliding, block_sizes, reps, random_state, allow_zeros=False)

Bootstrap the transformed BM-EI path on the full block-size grid.

bootstrap_bm_ei_path_draws(bootstrap_samples, *, block_sizes, path_keys=BM_PATH_KEYS, allow_zeros=False)

Transform one raw bootstrap bank into selected BM-EI z-path draw matrices.

estimate_native_bm_ei(bundle, *, base_path, sliding, use_adjusted_chandwich=False)

Estimate theta with a native single-block-size BM estimator.

estimate_pooled_bm_ei(bundle, *, base_path, sliding, regression, bootstrap_result=None, covariance_shrinkage=EI_DEFAULT_COVARIANCE_SHRINKAGE)

Estimate theta by pooling an observed BM path over a stable window.

prepare_ei_bundle(vec, *, block_sizes=None, threshold_quantiles=(0.9, 0.95), allow_zeros=False)

Prepare the observed-data ingredients reused across formal EI estimators.

plot_ei_fit(fit, *, file_path=None, dpi=1200, title=None, save=False, close=None)

Plot one EI fit either as a retained path view or a threshold summary.

plot_ei_path(path, *, file_path=None, dpi=1200, title=None, save=False, close=None, xlabel='log(block size)', ylabel='extremal index')

Plot one observed EI path together with its selected stable window.

extract_stable_path_window(path)

Return the selected stable block levels and transformed values for one path.

select_stable_path_window(block_sizes, z_path, *, min_points=4, trim_fraction=0.15, roughness_penalty=0.75, curvature_penalty=0.5)

Choose the most stable contiguous block-size window on the transformed EI path.

estimate_ferro_segers(bundle, *, threshold_quantiles=(0.9, 0.95))

Estimate theta with the Ferro-Segers intervals estimator.

estimate_k_gaps(bundle, *, threshold_quantiles=(0.9, 0.95), k_grid=(1, 2))

Estimate theta with the K-gaps likelihood.