Fuk-Nagaev Inequality in Smooth Banach Spaces: Optimum Bounds for Distributions of Heavy-Tailed Martingales
MCML Authors
Christian Fiedler
Dr.
Abstract
Christian Fiedler
Dr.
Abstract
We derive a Fuk-Nagaev inequality for the maxima of norms of martingale sequences in smooth Banach spaces which allow for a finite number of higher conditional moments. The bound is obtained by combining an optimization approach for a Chernoff bound due to Rio (2017) with a classical bound for moment generating functions of smooth Banach space norms by Pinelis (1994). Our result improves comparable infinite-dimensional bounds in the literature by removing unnecessary centering terms and giving precise constants. As an application, we propose a McDiarmid-type bound for vector-valued functions which allow for a uniform bound on their conditional higher moments.
BibTeXKey: MF25a