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New insights on concentration inequalities for self-normalized martingales. (English) Zbl 07126978
Summary: 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.
MSC:
60E15 Inequalities; stochastic orderings
60G42 Martingales with discrete parameter
60G15 Gaussian processes
60J80 Branching processes (Galton-Watson, birth-and-death, etc.)
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