Cramer type moderate deviations for self-normalized ψ-mixing sequences

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:486

Article

Fan, Xiequan¹ 

[1] Tianjin Univ, Ctr Appl Math, Tianjin 300072, Peoples R China

关键词: Cramer moderate deviations;    Self-normalized processes;    Studentized statistics;    Relative error;    Continued fraction expansions;   

DOI  :  10.1016/j.jmaa.2020.123902

来源: Elsevier

【 摘 要 】

Let (eta(i))(i >= 1) be a sequence of psi-mixing random variables. Let m = (sic)n(alpha)(sic), 0 < alpha < 1 k = [n/(2m)], and Y-j = Sigma(m)(i=1) eta(m(j-1)+i), 1 <= j <= k. Set S-k degrees = Sigma Y-k(j=1)j and [S degrees](kappa) = Sigma(k)(i=1) (Y-j)(2). We prove a Cramer type moderate deviation expansion for P(S-kappa degrees/root[S degrees](kappa) >= x) as n (R) infinity. Our result is similar to the recent work of Chen et al. (2016) [4] where the authors established Cramer type moderate deviation expansions for beta-mixing sequences. Comparing to the result of Chen et al., our results hold for mixing coefficients with polynomial decaying rate and wider ranges of validity. (C) 2020 Elsevier Inc. All rights reserved.

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