An overview of consistency results for depth functionals

Abstrakt

Data depth is a nonparametric tool which may serve as an extension of quantiles to general data. Any viable depth must posses the uniform strong consistency property of its sample version.

In this overview, a concise summary of the available uniform consistency results for most of the depths for functional data is given. Extensions of this theory towards random surfaces, imperfectly observed, and discontinuous functional data are studied.

Klíčová slova

• consistency
• depth
• functional data