Abstract
In this paper we establish consistency results for the sample h-mode depth in the general case of Banach-valued data. The rate of convergence is provided, which is linked to the rate at which the sample sequence of bandwidths converges to its population version.
The robustness of the h-mode depth, as well as the convergence of the associated modes of the distribution, is also studied. (C) 2015 Elsevier B.V. All rights reserved.