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

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:130

Article

Fan, Xiequan¹  Grama, Ion²  Liu, Quansheng²  Shao, Qi-Man³ 

[1] Tianjin Univ, Ctr Appl Math, Tianjin, Peoples R China

[2] Univ Bretagne Sud, LMBA, UMR CNRS 6205, Campus Tohannic, F-56017 Vannes, France

[3] Southern Univ Sci & Technol, Dept Stat & Data Sci, Shenzhen 518000, Peoples R China

关键词: Moderate deviations;    Stationary processes;    Cramer moderate deviations;   

DOI  :  10.1016/j.spa.2020.03.001

来源: Elsevier

【 摘 要 】

Let (X-i)(i >= 1) be a stationary sequence. Denote m = left perpendicularn(alpha)right perpendicular, 0 < alpha < 1, and k = left perpenducularn/mright perpendicular, where left perpendiculararight perpendicular stands for the integer part of a. Set S-j(o) = Sigma(m)(i=1) Xm(j-1)+i, 1 <= j <= k, and (V-k(o))(2) = Sigma(k)(j=1)(S-j(o))(2). We prove a Cramer type moderate deviation expansion for P(Sigma(k)(j=1) S-j(o)/V-k(o) >= x) as n -> infinity. Applications to mixing type sequences, contracting Markov chains, expanding maps and confidence intervals are discussed. (C) 2020 Elsevier B.V. All rights reserved.

【 授权许可】

Free