Band Depths Based on Multiple Time Instances

Abstract

Bands of vector-valued functions f:T↦Rd are defined by considering convex hulls generated by their values concatenated at m different values of the argument. The obtained m-bands are families of functions, ranging from the conventional band in case the time points are individually considered (for m=1 ) to the convex hull in the functional space if the number m of simultaneously considered time points becomes large enough to fill the whole time domain. These bands give rise to a depth concept that is new both for real-valued and vector-valued functions