We obtain the best possible upper bounds for the moments of a single-order statistic from independent, nonnegative random variables, in terms of the population mean. The main result covers the independent identically distributed case. Furthermore, the case of the sample minimum for merely independent (not necessarily identically distributed) random variables is treated in detail.

中文翻译：

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非负随机变量的阶统计的最优矩不等式

就总体均值而言，我们从独立的非负随机变量中获得单阶统计矩的最佳可能上界。主要结果涵盖了独立同分布的情况。此外，详细处理了仅针对独立（不一定同分布）随机变量的样本最小值的情况。