Exponential inequalities for self-normalized martingales with applications

TL;DR

This paper introduces new exponential inequalities for self-normalized martingales, extending existing results, and demonstrates their applications in linear regression, autoregressive, and branching processes.

Contribution

It presents novel exponential inequalities for self-normalized martingales and applies them to various stochastic process models.

Findings

New exponential inequalities for self-normalized martingales.

Applications demonstrated in linear regression, autoregressive, and branching processes.

Extension of De la Peña's inequalities to broader contexts.

Abstract

We propose several exponential inequalities for self-normalized martingales similar to those established by De la Pe\~{n}a. The keystone is the introduction of a new notion of random variable heavy on left or right. Applications associated with linear regressions, autoregressive and branching processes are also provided.