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Self-normalized central limit theorem and estimation of variance of partial sums for negative dependent random variables

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Abstract

Let {X n, n≥1} be a stationary LNQD or NA sequence satisfying EX 1 = μ, EX 21 <∞ and (Var S n)/n→σ2 as n→∞. In this paper a class of self-normalized central limit theorems and estimators of Var S n are studied. The weak and strong consistency of the estimators of Var S n are presented.

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Authors and Affiliations

  1. Dept. of Math., Zhejiang Univ., Xixi Campus, 310028, Hangzhou, China

    Zhang Lixin & Shi Strongway

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  1. Zhang Lixin
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  2. Shi Strongway
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Supported by the National Natural Science Foundation of China (10071072).

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Zhang, L., Shi, S. Self-normalized central limit theorem and estimation of variance of partial sums for negative dependent random variables. Appl. Math. Chin. Univ. 17, 326–334 (2002). https://doi.org/10.1007/s11766-002-0012-z

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  • DOI: https://doi.org/10.1007/s11766-002-0012-z

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