Abstract

We consider the order statistics \(X_{1:n},\ldots,X_{n:n}\) based on independent identically symmetrically distributed random variables. We determine sharp upper bounds in the properly centered linear combinations of order statistics \(\sum_{i=1}^{n}c_{i}(X_{i:n}-\mu)\), where \((c_{1},\ldots,c_{n})\) is an arbitrary vector of coefficients from the \(n\)-dimensional real space, and \(\mu\) is the symmetry center of the parent distribution, in various scale units. The scale units are constructed on the basis of absolute central moments of the parent distribution of various orders. The bounds are specified for single order statistics. The lower bounds are immediately concluded from the upper ones.

中文翻译：

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来自不同尺度单位的 Iid 对称群体的 $$\boldsymbol{L}$$ -statistics 的期望界限

摘要

我们考虑基于独立同对称分布随机变量的顺序统计量\(X_{1:n},\ldots,X_{n:n}\) 。我们在顺序统计的正确居中线性组合中确定尖锐的上限\(\sum_{i=1}^{n}c_{i}(X_{i:n}-\mu)\)，其中\((c_ {1},\ldots,c_{n})\)是来自\(n\)维实空间的任意系数向量，并且\(\mu\)是父分布的对称中心，在各种比例单位。尺度单元是根据各阶母分布的绝对中心矩构建的。边界是为单顺序统计指定的。下界立即从上界得出。