國立成功大學 統計學系

Two-sample functional data analysis is fundamental in various scientific fields, where accurate estimation and rigorous hypothesis testing are crucial for detecting differences between groups. An efficient sampling scheme is essential for enhancing estimation accuracy and test power. The optimal sampling design is formulated as a multi-objective optimization problem that balances trajectory recovery and hypothesis testing. The Pareto front is constructed to identify optimal trade-offs between these objectives. Moreover, a modified version of the SIB algorithm is proposed for its multi-objective purpose that significantly improves the efficiency of Pareto front approximation, outperforming existing methods in both convergence speed and solution quality. Through simulation studies and real-world applications, the effectiveness of the approach is demonstrated in enhancing both estimation and testing performance in two-sample functional data analysis.