Infinite Order U-statistics
将U统计量的核阶数扩展到依赖于样本大小，提出无限阶U统计量，证明其几乎必然相合性和渐近正态性，并通过重抽样解决计算问题，以Nelson风险函数估计等实例展示其应用。
A large class of estimators that is useful in the study of statistical inference is the class of U-statistics. A U-statistic is an extension of the concept of a sample mean; a U-statistic is the average over all possible evaluations of a function, called a kernel, of a random sample. In this paper, we extend this estimator by considering kernels whose order may depend upon the sample size and call the resulting estimator an infinite order U-statistic (IOUS). Certain basic properties, such as almost sure consistency, asymptotic normality and large sample interval estimates, are shown to hold. The extension to kernels of large order raises certain computational issues which are addressed via resampling techniques. To argue that the extension is practicable, several examples of IOUSs are provided. In some examples we write a known statistic, such as Nelson's hazard function estimator, as an IOUS. This representation automatically provides information about the bias of the estimator. Further, this type of representation suggests a natural truncation of para- meters that can be written as certain infinite sums.