Mathematical Sciences: Asymptotic Behavior of Mixing Sequenes of Random Variables and Applications

研究者将继续她的一些结构方面的研究和限制理论的相关随机变量与应用统计。这些变量的和的指数矩将在各种依赖假设下得到。研究结果将用于研究从平稳随机过程中抽样时密度核估计量和回归函数核估计量的一致一致性。对于不同类型的渐近独立随机变量，将得到新的弱极限定理。将寻求满足两部分混合条件的随机变量的极限定理，并将结果用于数据分析中使用的某些平滑过程输出的中心极限定理。对平稳强混合序列中心极限定理的Ibragimov-Iosifescu猜想进行了进一步的研究。

The investigator will continue her study of some structural aspects and limiting theory for dependent random variables with applications to statistics. Exponential moments of the sums of such variables will be found under various dependence assumptions. The results will be used to study the uniform consistency of kernel estimator of a density and of a regression function when sampling from a stationary stochastic process. New weak limit theorems will be obtained for various classes of asymptotically independent random variables. Limit theorems will be sought for random variables satisfying two-part mixing conditions and the results will be used for a central limit theorems for outputs of certain smoothing procedures used in data analysis. Progress will be made on the Ibragimov-Iosifescu conjecture of the central limit theorem of stationary strong mixing sequences.