Vestnik St. Petersburg University, Mathematics Pub Date : 2020-09-02 , DOI: 10.1134/s1063454120030061 O. I. Dudkina , N. V. Gribkova
Abstract
A theorem on the strong law of large numbers for linear functions of concomitants (induced order statistics) for sequences of independent identically distributed two-dimensional random vectors is proved in this paper. The result complements previous work by S.S. Yang (1981) and N. Gribkova and R. Zitikis (2017, 2019). The proof is based on the conditional independence property of the concomitants established by P. K. Bhattacharya (1974); the van Zwet strong law of large numbers for linear functions of order statistics (1980) is used and classical inequalities apply, including the Rosenthal inequality (1970).
中文翻译:
伴随线性组合的强大数定律
摘要
本文证明了关于独立同分布二维随机向量序列的伴随线性函数(诱导阶数统计)的强数定理。结果补充了SS Yang(1981)和N.Gribkova和R.Zitikis(2017,2019)的先前工作。证据是根据巴塔查亚(PK Bhattacharya)(1974)建立的伴随者的有条件独立性得出的;运用了范兹韦特的强数定律来处理阶数统计的线性函数(1980),并且应用了经典不等式,包括罗森塔尔不等式(1970)。