Laws of large numbers forL-statistics

RimasNorvai?a

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Laws of large numbers forL-statistics

机译：大数定律

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ConsiderLn=n?1∑1≤i≤ncnig(Xn:i)for order statisticsXn:iand letcni=n∫(i?1)iJdλfor some (Lebesgue)λ-summable over(0,1)functionJ. Sufficient as well as necessary conditions forlimnLn=∫01Jgdλto hold almost surely and in probability are given. Superposition(or Nemytskii) operators have been used to derive the laws of large numbers forL-statistics from the laws of large numbers in quasi-Banach function spaces for the empirical distribution functions based onX1,…,Xn.

机译：对于阶数统计量，考虑Ln = n？1∑1≤i≤ncnig（Xn：i）对于某些（Lebesgue）λ可叠加的（0,1）函数J，Xn：iand letcni =n∫（i？1）/ ni Jdλ。给出了几乎确定且有可能使limnLn =∫01Jgdλ的充分必要条件。对于基于X1，…，Xn的经验分布函数，已经使用叠加（或Nemytskii）运算符从拟Banach函数空间中的大数定律推导L统计量的大数定律。

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《International journal of stochastic analysis》 |1994年第2期|共19页
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RimasNorvai?a;
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Laws of large numbers forL-statistics

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