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Cook's Distance Measures for Varying Coefficient Models with Functional Responses.

Qibing Gao1, Mihye Ahn2, Hongtu Zhu2

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This study introduces new Cook's distance measures to identify influential data points and curves in functional response models. These diagnostics help improve the reliability of varying coefficient models in statistical analysis.

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Area of Science:

  • Statistics
  • Data Analysis
  • Functional Data Analysis

Background:

  • Varying coefficient models are widely used for analyzing complex functional data.
  • Assessing the influence of individual data points and curves is crucial for model diagnostics.
  • Existing diagnostic measures may not adequately capture the influence of atypical curves or multiple observations in functional settings.

Purpose of the Study:

  • To develop novel Cook's distance measures for identifying influential atypical curves and observations.
  • To extend diagnostic capabilities for varying coefficient models with functional responses.
  • To provide robust tools for assessing data influence in functional data analysis.

Main Methods:

  • Development of Cook's distance measures for deleting multiple curves and grid points.
  • Investigation of theoretical properties of the proposed diagnostic measures.
  • Conducting simulation studies to evaluate finite sample performance under various scenarios.

Main Results:

  • The proposed Cook's distance measures effectively identify influential atypical curves and observations.
  • Simulation results demonstrate the utility and robustness of the new diagnostic tools.
  • The measures provide valuable insights into data influence within functional response models.

Conclusions:

  • The developed Cook's distance measures enhance the diagnostic toolkit for varying coefficient models.
  • These measures are essential for ensuring the reliability and validity of functional data analyses.
  • Application to diffusion tensor tract data highlights practical utility in real-world scenarios.