| 负相依随机变量的自正则化中心极限定理与部分和的方差估计 |
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| 引用本文： | 张立新,施壮华. 负相依随机变量的自正则化中心极限定理与部分和的方差估计[J]. 高校应用数学学报(英文版), 2002, 17(3): 326-334. DOI: 10.1007/s11766-002-0012-z |
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| 作者姓名： | 张立新 施壮华 |
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| 作者单位： | Zhang Lixin Shi StrongwayDept.of Math.，Zhejiang Univ.，Xixi Campus，Hangzhou 310028，China. |
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| 基金项目： | the National Natural Science Foundation of China(1 0 0 71 0 72 ) |
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| 摘 要： | § 1 IntroductionWe firstintroduce some concepts.Random variables X and Y are called negative dependent ( ND) if for any pair ofmonotonically non-decresing functions f and g,Cov{ f( X) ,g( Y) }≤ 0 .Clearly itis equivalenttoP( X≤ x,Y≤ y)≤ P( X≤ x) P( Y≤ y)for all x,y∈R.A random sequence{ Xi,i≥ 1 } is said to be negative quadrant dependent( NQD) if any pairof variables Xi,Xj( i≠j) are ND.A sequence of random variables{ Xi,i≥ 1 } is said to be linear negative quadrand depend…
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| 收稿时间： | 2001-04-02 |
Self-normalized central limit theorem and estimation of variance of partial sums for negative dependent random variables |
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| Lixin Zhang,Strongway Shi. Self-normalized central limit theorem and estimation of variance of partial sums for negative dependent random variables[J]. Applied Mathematics A Journal of Chinese Universities, 2002, 17(3): 326-334. DOI: 10.1007/s11766-002-0012-z |
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| Authors: | Lixin Zhang Strongway Shi |
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| Affiliation: | (1) Dept. of Math., Zhejiang Univ., Xixi Campus, 310028 Hangzhou, China |
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| Abstract: | Let {X n, n≥1} be a stationary LNQD or NA sequence satisfying EX 1 = μ, EX 1 2 <∞ 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. Supported by the National Natural Science Foundation of China (10071072). |
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| Keywords: | estimation negative dependence consistency variance of partial sums. |
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