若干弱因变量的渐近结果

IF 0.4 Q4 STATISTICS & PROBABILITY Theory of Probability and Mathematical Statistics Pub Date : 2020-02-27 DOI:10.1090/TPMS/1077
Idir Arab, P. E. Oliveira
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引用次数: 2

摘要

研究一类控制在Lipschitz变换协方差上的弱相关随机变量。这一类包括但不限于正相关、负相关变量和其他一些弱相关结构。我们用收敛速率的特征证明了强大数定律,它几乎是最优的,在某种意义上,它是任意接近自变量的最优速率。此外,我们证明了一个比较联合分布与边际积分布的不等式,类似于众所周知的关联变量特征函数的纽曼不等式。结果证明了中心极限定理及其对应的泛函定理,并证明了这类弱因变量的经验过程的收敛性。
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Asymptotic results for certain weak dependent variables
We consider a special class of weak dependent random variables with control on covariances of Lipschitz transformations. This class includes, but is not limited to, positively, negatively associated variables and a few other classes of weakly dependent structures. We prove the Strong Law of Large Numbers with the characterization of convergence rates which is almost optimal, in the sense that it is arbitrarily close to the optimal rate for independent variables. Moreover, we prove an inequality comparing the joint distributions with the product distributions of the margins, similar to the well known Newman’s inequality for characteristic functions of associated variables. As a consequence, we prove the Central Limit Theorem together with its functional counterpart, and also the convergence of the empirical process for this class of weak dependent variables.
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来源期刊
CiteScore
1.30
自引率
0.00%
发文量
22
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