Visualization techniques are very useful in data analysis. Their aim is to summarize information into a graph or a plot. In particular, visualization is especially interesting when one has functional data, where there is no total order between the data of a sample. Taking into account the information provided by the down–upward partial orderings based on the hypograph and the epigragh indexes, we propose new strategies to analyze graphically functional data. In particular, combining the two indexes we get an alternative way to measure centrality in a bunch of curves, so we get an alternative measure to the statistical depth. Besides, motivated by the visualization in the plane of the two measures for two functional data samples, we propose new methods for testing homogeneity between two groups of functions. The performance of the tests is evaluated through a simulation study and we have applied them to several real data sets.

中文翻译：

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基于题词，符号和相关图形表示对功能数据进行等级测试

可视化技术在数据分析中非常有用。他们的目的是将信息汇总为图形或绘图。特别是当具有功能数据时，在样本数据之间没有总顺序的情况下，可视化尤为有趣。考虑到基于hypograph和epigragh索引的向下局部排序提供的信息，我们提出了分析图形功能数据的新策略。特别是，将这两个指标结合起来，便可以得到另一种方法来测量一堆曲线的中心度，因此可以得到一种替代方法来衡量统计深度。此外，受两个功能数据样本的两个度量平面中的可视化的启发，我们提出了测试两组功能之间同质性的新方法。