Some vector-valued examples of noncentral moderate deviation results

TL;DR

This paper explores vector-valued examples of noncentral moderate deviation principles, filling a gap between convergence in probability and non-Gaussian weak convergence in large deviation theory.

Contribution

It introduces new vector-valued examples of noncentral moderate deviations, extending existing real-valued results to higher dimensions.

Findings

Provides vector-valued examples of noncentral moderate deviations

Extends the theory from real-valued to vector-valued random variables

Highlights the applicability of noncentral moderate deviations in multivariate settings

Abstract

The term noncentral moderate deviations is used in the literature to mean a class of large deviation principles that, in some sense, fills the gap between the convergence in probability to a constant (governed by a reference large deviation principle) and a weak convergence to a non-Gaussian (and non-degenerating) distribution. Several examples can be found in the literature, mainly for real-valued random variables (see, e.g.,~\cite{GiulianoMacci} and the references cited therein). In this paper we present some examples with vector-valued random variables.