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

TL;DR

The paper introduces the GLD-plot, a new depth-based graphical tool for analyzing the unimodality of hyperspherical data, extending univariate ranks to directional data and comparing local and global depth measures.

Contribution

It proposes a novel local depth measure for hyperspherical data and visualizes it with the GLD-plot to assess unimodality, enhancing data analysis methods for directional data.

Findings

The GLD-plot effectively visualizes local and global data depth.

Simulation and real data examples demonstrate its utility.

The local depth provides insights into data structure.

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.