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A graphical tool for investigating the unimodality of hyperspherical data is proposed. It is based on the notion of statistical data depth function for directional data. A data depth extends the univariate concept of rank and leads to a natural centre-outward ordering of the sample points. First, a local version of distance-based depths for directional data is introduced. Then, the orderings induced by a local depth and its corresponding global version are compared by means of a two-dimensionalscatterplot, i.e., the GLD-plot (global-local depth plot). The graph can be easily visualized and interpreted. The proposal is evaluated on simulated and real data examples.

The GLD-plot: a depth-based graphical tool to investigate unimodality of directional data