Functional Data Analysis (FDA) is a statistical domain developed to handle functional data characterized by high dimensionality and complex data structures. Sequential Neural Networks (SNNs) are specialized neural networks capable of processing sequence data, a fundamental aspect of functional data. Despite their great flexibility in modeling functional data, SNNs have been inadequately employed in the FDA community. One notable advantage of SNNs is the ease of implementation, making them accessible to a broad audience beyond academia. Conversely, FDA-based methodologies present challenges, particularly for practitioners outside the field, due to their intricate complexity. In light of this, we propose utilizing SNNs in FDA applications and demonstrate their effectiveness through comparative analyses against popular FDA regression models based on numerical experiments and real-world data analysis. SNN architectures allow us to surpass the limitations of traditional FDA methods, offering scalability, flexibility, and improved analytical performance. Our findings highlight the potential of SNN-based methodologies as powerful tools for data applications involving functional data.

翻译：函数型数据分析（FDA）是一个为处理高维度和复杂数据结构函数型数据而发展的统计领域。序列神经网络（SNN）是能够处理序列数据的专用神经网络，而序列数据是函数型数据的基本特征。尽管SNN在函数型数据建模方面具有极大灵活性，但在FDA领域中的应用仍不充分。SNN的一个显著优势是其易于实现，这使得学术界之外的非专业人员也能便捷使用。相比之下，基于FDA的方法因其固有的复杂性而面临挑战，尤其对非专业从业者而言。基于此，我们提出在FDA应用中采用SNN，并通过数值实验和真实数据分析，将其与主流FDA回归模型进行对比分析以验证其有效性。SNN架构使我们能够突破传统FDA方法的局限，在可扩展性、灵活性和分析性能方面实现提升。研究结果表明，基于SNN的方法可作为函数型数据应用中强有力的分析工具。