On the hybrids of k-spacing empirical and partial sum processes

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• 作者：Sergio Alvarez-Andrade ; Salim Bouzebda
• 关键词：Hybrid process ; Spacing empirical process ; Order statistics ; Invariance principles ; Gaussian process ; Precise asymptotics ; Complete moment convergence ; Baum–Katz ; Convergence rates
• 刊名：Revista Matemática Complutense
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：30
• 期：1
• 页码：185-216
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics, general; Algebra; Analysis; Applications of Mathematics; Geometry; Topology;
• 出版者：Springer Milan
• ISSN：1988-2807
• 卷排序：30

文摘

The present paper is devoted to the study of the hybrids of k-spacing empirical and partial sum processes. In the first part, we present the gaussian approximation of these processes. In the second part, we obtain new results on the precise asymptotics in the law of the logarithm related to complete convergence and a.s. convergence, under some mild conditions, for the hybrids of k-spacing empirical and partial sum processes.