超越均值的一致估计

摘要：

有限样本界的估计误差的平均值的经验平均值，均匀的一类功能，往往可以方便地获得的Rademacher或高斯平均的类。如果n个变量的函数具有适当有界的偏导数，则它可以代替经验平均值，并且再次由高斯平均值控制均匀估计。一个常数的结果恢复标准结果的经验平均值和最近的U-统计量，并扩展到一般类的估计问题。

英文摘要：

Finite sample bounds on the estimation error of the mean by the empirical mean, uniform over a class of functions, can often be conveniently obtained in terms of Rademacher or Gaussian averages of the class. If a function of n variables has suitably bounded partial derivatives, it can be substituted for the empirical mean, with uniform estimation again controlled by Gaussian averages. Up to a constant the result recovers standard results for the empirical mean and more recent ones about U-statistics, and extends to a general class of estimation problems.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。