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

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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.