Local depth measures for distributions on the sphere

L. Fernández Piana, V. Moreno, M. Svarc, A. Justel Eusebio

In this work, we study three approaches for defining local depth measures for distributions on the sphere. We analyze their theoretical properties, including consistency, and complement this analysis with simulations to assess their empirical performance. The first approach is based on mapping points on $\mathbb{S}^p$ to their corresponding tangent planes via the logarithmic map, where local depth is computed in the projected space. The second approach follows an integrated depth framework, where univariate local depth values are computed on randomly sampled great circles and then averaged. The third approach is based on randomly sampled great circles that induce hemispherical caps, on which local depths are computed in a manner analogous to the circular setting.

Palabras clave: Local Depth, Spherical Data, Circular Data

Estadística No Paramétrica
3 de septiembre de 2026  11:10
Aula 29

J. M. de Frutos Porras

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