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Automatic detection of significant areas for functional data with directional error control.

Peirong Xu1, Youngjo Lee2, Jian Qing Shi3

  • 1College of Mathematics and Sciences, Shanghai Normal University, Shanghai, China.

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This study introduces an automated method for identifying significant differences between curve samples. The procedure offers optimal control of directional errors and is computationally efficient for complex data.

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Area of Science:

  • Statistics
  • Biostatistics
  • Data Analysis

Background:

  • Identifying significant differences between sample curves is crucial in various scientific fields.
  • Existing methods may lack efficiency or struggle with complex data structures.

Purpose of the Study:

  • To develop a large-scale multiple testing procedure for automatically detecting significant sub-areas between two samples of curves.
  • To ensure the procedure is optimal, computationally inexpensive, and handles multidimensional covariates and varied sampling designs.

Main Methods:

  • A novel large-scale multiple testing procedure.
  • Nonparametric Gaussian process regression model for two-sided multiple tests.
  • Introduction of a 'significant curve/surface' concept.

Main Results:

  • The procedure asymptotically controls the directional false discovery rate at any specified level.
  • Demonstrated superior performance in simulations with strong power and good directional error control.
  • Successfully applied to executive function studies in hemiplegia.

Conclusions:

  • The proposed method provides an efficient and robust approach for analyzing differences between curve samples.
  • Offers valuable insights into dynamic significant differences, applicable to real-world scientific problems.