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

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.