ABSTRACT

When analyzing functional data processes, the presence of outliers can greatly influence modelling and forecasting outcomes and lead to the inaccurate conclusion. Hence, detection of such outliers becomes an essential task. Visualization of data not only plays a vital role in discovering the features of data before applying statistical models and summary statistics but also provides an auxiliary tool in identifying outliers. The research involving visualization and sensitivity analysis for functional data has not yet received much attention in the literature to date. Thus, this becomes the focus of this paper. To this end, we propose a method combining influence function with iteration scheme for identifying outliers and develop new visualization tools for displaying features and grasping the outliers in functional data. Furthermore, comparisons between our proposed methods with the existing methods are also investigated. Finally, we illustrate these proposed methods with simulation studies and real data examples.

摘要

在分析功能数据过程时，异常值的存在会极大地影响建模和预测结果，并导致得出不正确的结论。因此，检测这些异常值成为一项必不可少的任务。数据的可视化不仅在应用统计模型和摘要统计之前发现数据的特征方面起着至关重要的作用，而且还提供了识别异常值的辅助工具。迄今为止，涉及功能数据的可视化和敏感性分析的研究尚未受到文献的广泛关注。因此，这成为本文的重点。为此，我们提出了一种将影响函数与迭代方案相结合的方法来识别离群值，并开发了新的可视化工具来显示特征并掌握功能数据中的离群值。此外，还研究了我们提出的方法与现有方法之间的比较。最后，我们通过仿真研究和实际数据示例来说明这些建议的方法。