Bootstrap-based inference on the difference in the means of two correlated functional processes

Area of Science:

• Statistics
• Biostatistics
• Neuroscience

Background:

• Correlated functional data analysis is crucial in various scientific fields.
• Accurate inference on mean differences is essential for comparative studies.
• Sleep electroencephalograms (EEGs) provide complex, correlated functional data.

Purpose of the Study:

• To propose and evaluate nonparametric inference methods for the mean difference between two correlated functional processes.
• To compare different smoothing and estimation strategies for mean and covariance functions.
• To apply these methods to analyze sleep EEG data in severe sleep apnea patients versus controls.

Main Methods:

• Nonparametric inference for mean difference in correlated functional data.
• Comparison of methods incorporating varying levels of smoothing for mean and covariance.
• Preservation of sampling design in statistical analysis.
• Utilizing both parametric and nonparametric estimation of mean functions.
• Application to sleep electroencephalogram (EEG) data from the Sleep Heart Health Study.

Main Results:

• The proposed nonparametric methods provide robust inference on the mean difference between correlated functional processes.
• Different smoothing and estimation techniques yield comparable results in the case study.
• The analysis identified specific differences in sleep EEG δ power between severe sleep apnea patients and controls.

Conclusions:

• The developed nonparametric methods are effective for analyzing correlated functional data, particularly in biomedical applications.
• These methods offer a flexible framework applicable to diverse studies involving complex functional data.
• The findings contribute to understanding sleep disturbances in severe sleep apnea.