A Powerful Global Test Statistic for Functional Statistical Inference.

Area of Science:

• Statistics
• Bioinformatics
• Genetics

Background:

• Association testing between functional data and scalar variables is crucial in various scientific fields.
• Existing methods may struggle with aggregating weak signals and high dimensionality inherent in functional data.

Purpose of the Study:

• To develop a robust statistical framework for association testing in a varying coefficient model setting.
• To propose a functional projection regression model and a global test statistic for enhanced signal detection and dimension reduction.

Main Methods:

• A functional projection regression model is proposed, utilizing a global test statistic to aggregate signals across the functional data domain.
• An optimal functional projection direction is selected via ridge penalty to maximize signal-to-noise ratio.
• Asymptotic distribution of the test statistic is theoretically analyzed, with a strategy for adaptive tuning parameter selection.

Main Results:

• Simulations demonstrate that the proposed test significantly outperforms current state-of-the-art methods in functional statistical inference.
• The method effectively aggregates weak signals and reduces dimensionality in functional data analysis.

Conclusions:

• The developed functional projection regression model provides a powerful new tool for association testing.
• The method shows promise for applications in complex genetic studies, such as genome-wide association analysis of imaging genetic data.