Data depths satisfying the projection property

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On the Concept of Depth for Functional Data (2009, methodology): “Dyckerhoff (2004) also considered desirable properties for multivariate depths. Data depth can be widely applied. For example, Liu and Singh (1993) presented a nonparametric multivariate rank test using a quality depth index and Liu (1995) proposed control charts for multivariate processes using dep”
Choosing Among Notions of Multivariate Depth Statistics (2020, background): “For example, the halfspace depth and the projection depth satisfy the projection property, as well as the zonoid depth and the Mahalanobis depth; see Dyckerhoff (2004).”