Abstract

The necessary and sufficient conditions are found for convergences of series of weighted probabilities of large deviations for combinatorial sums \(\sum\nolimits_i {{{X}_{{ni{{\pi }_{n}}(i)}}}} \), where ||X_nij|| is an n-order matrix of independent random variables and (π_n(1), π_n(2), …, π_n(n)) is a random permutation with the uniform distribution on the set of permutations of numbers 1, 2, …, n independent of X_nij. Combinatorial variants of the results of convergence rates are obtained in the strong law of large numbers and in the law of the iterated logarithm under close to optimal conditions. Applications to rank statistics are discussed.

中文翻译：

---

组合强极限定理的收敛速度界及其应用

摘要

为组合和\（\ sum \ nolimits_i {{{X} _ {{ni {{\ pi} _ {n}}（i）}}的大偏差加权加权序列的收敛找到必要的充分条件}} \），其中|| X _nij || 是Ñ阶独立随机变量的矩阵和（π _Ñ（1），π _Ñ（2），...，π _Ñ（Ñ））是与所设置的数字1，2的排列中的均匀分布的随机排列，…，n独立于X _nij。收敛速度结果的组合变式是在接近最佳条件的情况下，以大量的强定律和迭代对数定律获得的。讨论了对统计排名的应用。