https://github.com/jedrzej-wydra/independence
Independence of functional data
https://github.com/jedrzej-wydra/independence
functional-data-analysis gpu-computing independence-of-functional-data
Last synced: about 1 year ago
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Independence of functional data
- Host: GitHub
- URL: https://github.com/jedrzej-wydra/independence
- Owner: Jedrzej-Wydra
- Created: 2024-08-17T22:34:05.000Z (almost 2 years ago)
- Default Branch: main
- Last Pushed: 2024-12-04T21:25:54.000Z (over 1 year ago)
- Last Synced: 2025-01-28T18:15:59.571Z (over 1 year ago)
- Topics: functional-data-analysis, gpu-computing, independence-of-functional-data
- Language: Jupyter Notebook
- Homepage:
- Size: 4.74 MB
- Stars: 0
- Watchers: 1
- Forks: 0
- Open Issues: 0
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Metadata Files:
- Readme: README.md
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README
# Distance of Mean Embedding for Testing Independence of Functional Data
#### authors: Mirosław Krzyśko, Łukasz Smaga, Jędrzej Wydra
## Abstract
We investigate independence testing for functional data, which may be either univariate or multivariate. Broadly speaking, our approach involves first reducing the dimensionality of the functional data using basis expansion and then applying the distance of mean embedding - a flexible measure of independence. We enhance this method for pairwise independence by incorporating marginal aggregation, as well as asymmetric and symmetric aggregation measures, to improve test performance and adapt it to mutual independence testing. Our methods are compared with tests based on distance covariance and the Hilbert-Schmidtindependence criterion. To evaluate their effectiveness, we present simulation studies and two real data examples using air pollution and chemometric data sets. The new testing procedures demonstrate favorable finite-sample properties, effectively controlling the type I error rate and exhibiting competitive power, making them viable alternatives to covariance-based tests.
## Preprint hyperlink
You can access the preprint here: [Distance of Mean Embedding for Testing Independence of Functional Data]([https://doi.org/10.48550/arXiv.2409.09516](https://dx.doi.org/10.2139/ssrn.5019416))
## History
This project is truly a dream come true for me — it’s all about developing a new test for the independence of functional data. But, of course, with great dreams come great challenges. First, designing new statistical tests is no walk in the park; it’s more like navigating a maze in the dark. Second, functional data is notoriously tricky — working with it feels like trying to solve a puzzle where the pieces keep changing shape. Despite these hurdles, I’m thrilled to tackle this project, knowing that if it succeeds, it could make a significant impact in the field.