Self-normalized Cramér type moderate deviations for martingales

Self-normalized Cramér type moderate deviations for martingales

Let (Xi, ℱi)i≥1 be a sequence of martingale differences. Set S n = Σ i = 1 n X i and S n = Σ i = 1 n   X i 2 . We prove a Cramér type moderate deviation expansion for P S n / S n ≥ x as n ➝ + ∞. Our results partly extend the earlier work of Jing, Shao and Wang (Ann. Probab. 31 (2003) 2167–2215) for...

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Veröffentlicht in:Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability 2019-11, Vol.25 (4A), p.2793-2823
Hauptverfasser: FAN, XIEQUAN, GRAMA, ION, LIU, QUANSHENG, SHAO, QI-MAN
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container_title Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability
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creator FAN, XIEQUAN
GRAMA, ION
LIU, QUANSHENG
SHAO, QI-MAN
description Let (Xi, ℱi)i≥1 be a sequence of martingale differences. Set S n = Σ i = 1 n X i and S n = Σ i = 1 n   X i 2 . We prove a Cramér type moderate deviation expansion for P S n / S n ≥ x as n ➝ + ∞. Our results partly extend the earlier work of Jing, Shao and Wang (Ann. Probab. 31 (2003) 2167–2215) for independent random variables.
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subjects Mathematics
Probability
title Self-normalized Cramér type moderate deviations for martingales
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