Weak convergence of discretely observed functional data with applications

Abstrakt

A general result on weak convergence of the empirical measure of discretely observed functional data is shown. It is applied to the problem of estimation of functional mean value, and the problem of consistency of various types of depth for functional data.

Counterexamples illustrating the fact that the assumptions as stated cannot be dropped easily are given.

Klíčová slova

• Consistency
• Data depth
• Functional data
• Functional moments
• Weak convergence