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2019 New insights on concentration inequalities for self-normalized martingales
Bernard Bercu, Taieb Touati
Electron. Commun. Probab. 24: 1-12 (2019). DOI: 10.1214/19-ECP269

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.

Citation

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Bernard Bercu. Taieb Touati. "New insights on concentration inequalities for self-normalized martingales." Electron. Commun. Probab. 24 1 - 12, 2019. https://doi.org/10.1214/19-ECP269

Information

Received: 14 June 2019; Accepted: 4 October 2019; Published: 2019
First available in Project Euclid: 12 October 2019

zbMATH: 07126978
MathSciNet: MR4029432
Digital Object Identifier: 10.1214/19-ECP269

Subjects:
Primary: 60E15, 60G42
Secondary: 60G15, 60J80

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