The GLD-plot: A depth-based plot to investigate unimodality of directional data

Abstract

A graphical tool for investigating unimodality of hyperspherical data is proposed. It is based on the notion of statistical data depth function for directional data which extends the univariate concept of rank. Firstly a local version of distance-based depths for directional data based on aims at analyzing the local structure of hyperspherical data is proposed. Then such notion is compared to the global version of data depth by means of a two-dimensional scatterplot, i.e. the GLD-plot. The proposal is illustrated on simulated and real data examples.