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Testing homogeneity: the trouble with sparse functional data.

Changbo Zhu1, Jane-Ling Wang2

  • 1Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, Notre Dame, United States.

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|July 31, 2023
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Summary
This summary is machine-generated.

This study introduces a new statistical test for comparing two samples of functional data, even when measurements are sparse. The proposed method, based on energy distance, effectively tests for marginal homogeneity in functional data analysis.

Keywords:
convergence rateenergy distancelongitudinal datameasurement errorssparse functional datatwo-sample test

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Area of Science:

  • Statistics
  • Functional Data Analysis

Background:

  • Comparing functional data samples is crucial but challenging, especially with sparse measurements.
  • Existing methods often struggle with the complexities of sparsely measured functional data.

Purpose of the Study:

  • To address the challenges of testing homogeneity in sparsely measured functional data.
  • To propose a novel two-sample statistic applicable to both intensive and sparse functional data.

Main Methods:

  • Developing a new test statistic based on energy distance.
  • Analyzing the convergence rate of the test statistic and consistency of permutation tests.
  • Investigating the feasibility of testing marginal homogeneity using point-wise distributions under mild constraints.

Main Results:

  • The proposed energy distance-based statistic is effective for both intensively and sparsely measured functional data.
  • Theoretical guarantees for the test statistic's convergence and permutation test consistency are established.
  • The method demonstrates practical applicability on synthetic and real-world datasets.

Conclusions:

  • The novel statistical test provides a robust solution for comparing functional data samples, accommodating sparsity.
  • The approach enhances the capabilities of functional data analysis, particularly in scenarios with limited measurements.