任意函数glivenko-cantelli类及其对不同依赖类型的应用

Far East Journal of Theoretical Statistics Pub Date : 2019-07-05 DOI:10.17654/ts060020041

H. Sangaré, G. Lo, M. Traore

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引用次数: 1

摘要

利用Sangar\ e和Lo(2015)证明的一般强大数定律和熵数，我们为任意平稳实值随机变量(rrv’s)提供了函数Glivenko-Cantelli (GC)类。接下来，针对不同类型的依赖(特别是关联，$\phi$混合)对一般结果进行了具体说明，并与文献中的现有结果进行了比较。

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ARBITRARY FUNCTIONAL GLIVENKO-CANTELLI CLASSES AND APPLICATIONS TO DIFFERENT TYPES OF DEPENDENCE

Using a general strong law of large number proved by Sangar\'e and Lo (2015) and the entropy numbers, we provide functional Glivenko-Cantelli (GC) classes for arbitrary stationary real-valued random variables (rrv's). Next, the general results are particularized for different types of dependence (association, $\phi$-mixing, in particular) and compared with available results in the literature.

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Far East Journal of Theoretical Statistics

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