Mathematical Sciences: Asymptotic Behavior of Dependent Sequences of Random Variables and Applications

本研究探讨具有各种相依性之随机变数序列之渐近性质。 通过将弱相依序列与半鞅和半鞅联系起来，我们将阐明这些序列几乎处处收敛的某些方面。这项研究的另一部分 将研究基于相依数据的样本均值方差的两个估计量。这些估计建议的分块技术和强大的统计程序，如引导和刀切。该估计量可用作中心极限定理中的自正规化器。 统计学的主要问题之一是对某些未知参数给出区间估计。这些置信区间是基于参数的估计量和该估计量的可变性给出的误差构建的。本研究的目的是在数据相依的情况下研究这一问题。

This research involves the investigation of the asymptotic properties of sequences of random variables with various types of dependence. By relating weak dependent sequences to semiamarts and demimartingales we shall clarify some aspects of the almost sure convergence of these sequences. Other part of this research will study two estimators of the variance of the sample mean based on dependent data. These estimators are suggested by blocking techniques and robust statistical procedures such as the bootstrap and the jackknife. The estimators can be used as selfnormalizers in the Central Limit Theorem. One of the main problems of statistics is to provide interval estimates for some unknown parameters. These confidence intervals are constructed based on an estimator of the parameter and an error given by the variability of this estimator. The purpose of this research is to study this problem in the case when the data is dependent.