Self-normalized Cramér type moderate deviations for stationary sequences and applications

Xiequan Fan, Ion Grama, Quansheng Liu and Qi-Man Shao

Stochastic Processes and their Applications, 2020, vol. 130, issue 8, 5124-5148

Abstract: Let (Xi)i≥1 be a stationary sequence. Denote m=⌊nα⌋,0<α<1, and k=⌊n∕m⌋, where ⌊a⌋ stands for the integer part of a. Set Sj∘=∑i=1mXm(j−1)+i,1≤j≤k, and (Vk∘)2=∑j=1k(Sj∘)2. We prove a Cramér type moderate deviation expansion for P(∑j=1kSj∘∕Vk∘≥x) as n→∞. Applications to mixing type sequences, contracting Markov chains, expanding maps and confidence intervals are discussed.

Keywords: Moderate deviations; Stationary processes; Cramér moderate deviations (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0304414919304314
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:130:y:2020:i:8:p:5124-5148

Ordering information: This journal article can be ordered from
http://http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

DOI: 10.1016/j.spa.2020.03.001

Access Statistics for this article

Stochastic Processes and their Applications is currently edited by T. Mikosch

More articles in Stochastic Processes and their Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().