[ENH] Implement LOESS Smoother (Locally Estimated Scatterplot Smoothing)

[Nithurshen]

Reference Issues/PRs

Fixes #2974

What does this implement/fix? Explain your changes.

Implementation Details:

• Class: LoessSmoother extending BaseSeriesTransformer.
• Parameters:
  • span: Float (0, 1] defining the proportion of data used in the local window.
  • degree: Int (1 or 2) defining the local polynomial degree (Linear or Quadratic).
• Multivariate Support: Iterates over channels while reusing the Design Matrix ($H$) and Weight Matrix ($W$) for the time axis to improve efficiency.
• Safety: Includes input validation for parameters and a fallback check for very short time series ($n \le degree$).
• Tests: Added test_loess.py covering:
  • Linear and Quadratic function recovery.
  • Constant value preservation.
  • Noise reduction effectiveness (MSE decrease on noisy sine waves).
  • Edge cases (short series, extreme span values).

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

No

Any other comments?

Reference:
[1] Cleveland, W. S. (1979). Robust locally weighted regression and smoothing scatterplots. Journal of the American statistical association, 74(368), 829-836.

• Performance: The current implementation uses NumPy vectorization. While it is efficient for typical time series lengths, the core loop is Python-bound. I am happy to convert the solver loop to a Numba-optimized function if performance gain is needed for this iteration.

PR checklist

For all contributions

• I've added myself to the list of contributors. Alternatively, you can use the @all-contributors bot to do this for you after the PR has been merged.
• The PR title starts with either [ENH], [MNT], [DOC], [BUG], [REF], [DEP] or [GOV] indicating whether the PR topic is related to enhancement, maintenance, documentation, bugs, refactoring, deprecation or governance.

For new estimators and functions

• I've added the estimator/function to the online API documentation.
• (OPTIONAL) I've added myself as a __maintainer__ at the top of relevant files and want to be contacted regarding its maintenance. Unmaintained files may be removed. This is for the full file, and you should not add yourself if you are just making minor changes or do not want to help maintain its contents.

For developers with write access

• (OPTIONAL) I've updated aeon's CODEOWNERS to receive notifications about future changes to these files.

[aeon-actions-bot]

Thank you for contributing to aeon

I have added the following labels to this PR based on the title: [ enhancement ].
I have added the following labels to this PR based on the changes made: [ transformations ]. Feel free to change these if they do not properly represent the PR.

The Checks tab will show the status of our automated tests. You can click on individual test runs in the tab or "Details" in the panel below to see more information if there is a failure.

If our pre-commit code quality check fails, any trivial fixes will automatically be pushed to your PR unless it is a draft.

Don't hesitate to ask questions on the aeon Slack channel if you have any.

PR CI actions

These checkboxes will add labels to enable/disable CI functionality for this PR. This may not take effect immediately, and a new commit may be required to run the new configuration.

• Run pre-commit checks for all files
• Run mypy typecheck tests
• Run all pytest tests and configurations
• Run all notebook example tests
• Run numba-disabled codecov tests
• Stop automatic pre-commit fixes (always disabled for drafts)
• Disable numba cache loading
• Regenerate expected results for testing
• Push an empty commit to re-run CI checks