New insights on concentration inequalities for self-normalized martingales

TL;DR

This paper introduces improved concentration inequalities for self-normalized martingales by using a weighted sum of quadratic variations, enhancing flexibility and applicability in various statistical contexts.

Contribution

The paper presents novel concentration inequalities for self-normalized martingales using a weighted sum of quadratic variations, improving upon previous bounds.

Findings

Enhanced concentration inequalities with better bounds.

Applicability to autoregressive processes and diffusion-limited aggregation.

Demonstrated usefulness in online statistical learning.

Abstract

We propose new concentration inequalities for self-normalized martingales. The main idea is to introduce a suitable weighted sum of the predictable quadratic variation and the total quadratic variation of the martingale. It offers much more flexibility and allows us to improve previous concentration inequalities. Statistical applications on autoregressive process, internal diffusion-limited aggregation process, and online statistical learning are also provided.