Mixed Gaussian Projections for Two-Sample Testing of Functional Data
This study addresses the limited power of existing two-sample tests for functional data in finite-sample settings by proposing a hybrid Gaussian random projection method that integrates Haar and Fourier Gaussian components to simultaneously capture local discontinuities and global oscillatory differences. The approach innovatively incorporates a label-invariant, data-adaptive covariance operator, enhancing detection sensitivity while preserving the validity of permutation-based inference. Theoretical analysis establishes the consistency of the proposed test, and empirical evaluations demonstrate its strong specificity and robustness in simulations. When applied to the ECG5000 dataset, the method effectively identifies class distinctions primarily driven by local features and significantly outperforms competing approaches, particularly in scenarios involving changes in covariance structure.