Open Access
August 2016 Self-normalized Cramér-type moderate deviations under dependence
Xiaohong Chen, Qi-Man Shao, Wei Biao Wu, Lihu Xu
Ann. Statist. 44(4): 1593-1617 (August 2016). DOI: 10.1214/15-AOS1429


We establish a Cramér-type moderate deviation result for self-normalized sums of weakly dependent random variables, where the moment requirement is much weaker than the non-self-normalized counterpart. The range of the moderate deviation is shown to depend on the moment condition and the degree of dependence of the underlying processes. We consider three types of self-normalization: the equal-block scheme, the big-block-small-block scheme and the interlacing scheme. Simulation study shows that the latter can have a better finite-sample performance. Our result is applied to multiple testing and construction of simultaneous confidence intervals for ultra-high dimensional time series mean vectors.


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Xiaohong Chen. Qi-Man Shao. Wei Biao Wu. Lihu Xu. "Self-normalized Cramér-type moderate deviations under dependence." Ann. Statist. 44 (4) 1593 - 1617, August 2016.


Received: 1 April 2015; Revised: 1 December 2015; Published: August 2016
First available in Project Euclid: 7 July 2016

zbMATH: 1359.62060
MathSciNet: MR3519934
Digital Object Identifier: 10.1214/15-AOS1429

Primary: 60F10 , 62E20

Keywords: absolutely regular , Cramér-type moderate deviation , functional dependence measures , ultra-high dimensional time series

Rights: Copyright © 2016 Institute of Mathematical Statistics

Vol.44 • No. 4 • August 2016
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