feat(moments): add sample_weight support to EmpiricalCovariance - #417

Reference Issues/PRs

Fixes #416. Builds on the sample-weight helpers from #412.

What does this implement/fix? Explain your changes.

Adds sample_weight to EmpiricalCovariance.fit, following the points in #416:

• Validation and scale invariance: weights go through _validate_sample_weight and are rescaled with _normalize_sample_weight, so only relative sizes matter. Zero weights drop observations.
• Location and assume_centered: the location is the weighted mean, or zero when assume_centered=True.
• window_size: weights are validated against the full X, then sliced with the same apply_window_size call, so they stay aligned with the last window_size observations.
• ddof: the weighted second moment is divided by 1 - ddof * sum(w**2) (weights summing to one). For ddof=0 this is the distributional covariance; for ddof=1 it is the reliability-weights correction already used by _weighted_variance and by np.cov(..., aweights=...). For uniform weights it reduces to n - ddof and matches the existing unweighted results.
• Errors: all-zero weights, and weights whose effective number of observations 1 / sum(w**2) is not greater than ddof, raise a ValueError with an explicit message.
• Routing: since fit now takes sample_weight, it can be requested with set_fit_request(sample_weight=True); a test checks it through CovarianceDistance and HierarchicalRiskParity.
• Docs: the docstring explains ddof with weights and adds a Notes section on distributional versus sample-corrected covariance, saying that the correction does not by itself justify an unbiasedness claim for arbitrary scenario probabilities.

Default path: when sample_weight is None the code path is unchanged; the only addition is two is not None checks. Fit time on main vs this branch (best of 7 × 50 fits): 0.908 vs 0.905 ms for 2000×100, 0.103 vs 0.103 ms for 250×20.

Does your contribution introduce a new dependency? If yes, which one?

No.

What should a reviewer concentrate their feedback on?

The ddof convention with weights and the wording of the Notes section.

Any other comments?

Tests cover: uniform weights matching the unweighted estimator (ddof 0/1/3, assume_centered, window_size), agreement with np.cov(aweights=...), assume_centered, scale invariance, integer weights equal to repeated rows, zero weights, window slicing, a single asset, invalid weights, and routing through CovarianceDistance and HierarchicalRiskParity. All 26 new tests fail on main.

Locally: ruff check, ruff format, ty check and deptry src pass. The full suite passes except 34 tests (33 SCIP-based tests in test_mean_risk.py and the OpinionPooling doctest) that fail identically on main in my environment.

PR checklist

For all contributions

• The PR title follows Conventional Commits, for example fix(portfolio): ..., with a type listed in CONTRIBUTING.md.
• New behavior and bug fixes are covered by tests.
• The tests and code quality checks pass locally.
• The documentation is updated when behavior or public APIs change.