Functional data analysis has gained significant attention due to its wide applicability. This research explores the extension of statistical analysis methods for functional data, with a primary focus on supervised classification techniques. It provides a review on the existing depth-based methods used in functional data samples. Building on this foundation, it introduces an extremality-based approach, which takes the modified epigraph and hypograph indexes properties as classification techniques. To demonstrate the effectiveness of the classifier, it is applied to both real-world and synthetic data sets. The results show its efficacy in accurately classifying functional data. Additionally, the classifier is used to analyze the fluctuations in the S\&P 500 stock value. This research contributes to the field of functional data analysis by introducing a new extremality-based classifier. The successful application to various data sets shows its potential for supervised classification tasks and provides valuable insights into financial data analysis.

翻译：函数型数据分析因其广泛适用性而受到显著关注。本研究探索了函数型数据统计分析方法的扩展，主要聚焦于监督分类技术。本文综述了现有基于深度的方法在函数型数据样本中的应用。在此基础上，提出了一种基于极值性的方法，该方法将修正的图上与图下指数特性作为分类技术。为验证分类器的有效性，将其应用于真实世界和合成数据集。结果表明该方法能有效实现函数型数据的准确分类。此外，该分类器被用于分析标普500股票价值的波动。本研究通过引入一种新的基于极值性的分类器，为函数型数据分析领域做出了贡献。在多种数据集上的成功应用展示了其在监督分类任务中的潜力，并为金融数据分析提供了有价值的见解。