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Domain selection and familywise error rate for functional data: A unified framework.

Konrad Abramowicz1, Alessia Pini2, Lina Schelin3

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Biometrics
|March 30, 2022
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Summary

This study introduces a unified framework for functional data domain selection, enhancing statistical inference. A novel thresholdwise testing approach offers data-driven domain selection, improving upon existing methods for complex datasets.

Keywords:
adjusted p-value functionfunctional datalocal inferencepermutation test

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Area of Science:

  • Statistics
  • Functional Data Analysis
  • Machine Learning

Background:

  • Functional data analysis deals with infinite-dimensional data, requiring specialized domain selection techniques.
  • Existing methods for domain selection in functional data often rely on predefined subset families.
  • Controlling the familywise error rate (FWER) is crucial for reliable inference in multiple testing scenarios.

Purpose of the Study:

  • To present a unified statistical testing framework for domain selection in functional data analysis.
  • To introduce a novel data-driven approach, thresholdwise testing, for functional domain selection.
  • To generalize domain selection methods to multidimensional functional data.

Main Methods:

  • Developing a unified framework for hypothesis testing on functional data subsets.
  • Adjusting pointwise p-values to control the familywise error rate (FWER) across families of subsets.
  • Proposing thresholdwise testing, a data-driven method for constructing subset families.
  • Extending the framework to handle multidimensional functional domains.

Main Results:

  • Demonstrated that existing state-of-the-art domain selection methods can be integrated into the unified framework.
  • Established theoretical guarantees for consistency and FWER control within the proposed framework.
  • Showcased the effectiveness of thresholdwise testing, particularly for multidimensional data.
  • Validated the methods through simulations and real-world data analysis.

Conclusions:

  • The unified framework provides a flexible and robust approach to functional data domain selection.
  • Thresholdwise testing offers a powerful, data-driven alternative that generalizes well to complex data structures.
  • The proposed methods advance the field of functional data analysis by improving inference and domain selection capabilities.