Resampling-based multiple comparison procedure with application to point-wise testing with functional data

Area of Science:

• Statistics
• Functional Data Analysis
• Environmental Science

Background:

• Correlated test statistics are common in functional linear models, posing challenges for traditional multiple testing procedures.
• Existing methods like Fisher's and Šidák's corrections have limitations when dealing with dependent test results.

Purpose of the Study:

• To develop a coherent multiple testing procedure specifically designed for correlated test statistics in functional linear models.
• To enhance the accuracy and reliability of statistical inference in complex data settings.

Main Methods:

• The procedure integrates resampling techniques to estimate p-values for correlated Fisher's and Šidák's test statistics.
• A novel test statistic, the smallest p-value, is proposed and combined with the closure principle for overall and individual p-value adjustments.
• A computationally efficient shortcut version is presented for scenarios involving a large number of tests.

Main Results:

• A simulation study demonstrated the proposed methodology's effectiveness in handling correlated tests within functional linear models.
• The procedure successfully controls error rates while maintaining statistical power in simulated correlated data.

Conclusions:

• The developed multiple testing procedure offers a robust solution for analyzing correlated functional data.
• The method is applicable to real-world environmental studies, such as detecting vegetation stress from CO2 leakage using spectral data.