Electronic Communications in Probability

New insights on concentration inequalities for self-normalized martingales

Bernard Bercu and Taieb Touati

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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.

Article information

Electron. Commun. Probab., Volume 24 (2019), paper no. 63, 12 pp.

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

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Primary: 60E15: Inequalities; stochastic orderings 60G42: Martingales with discrete parameter
Secondary: 60G15: Gaussian processes 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)

concentration inequalities martingales autoregressive process statistical learning

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Bercu, Bernard; Touati, Taieb. New insights on concentration inequalities for self-normalized martingales. Electron. Commun. Probab. 24 (2019), paper no. 63, 12 pp. doi:10.1214/19-ECP269. https://projecteuclid.org/euclid.ecp/1570845629

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