CLT FOR U-STATISTICS WITH GROWING DIMENSION

被引：4

作者：

DiCiccio, Cyrus ^{[1
]}

Romano, Joseph ^{[2
,3
]}

机构：

[1] LinkedIn Corp, 1000 W Maude Ave, Sunnyvale, CA 94085 USA

[2] Stanford Univ, Dept Stat, Sequoia Hall, Stanford, CA 94305 USA

[3] Stanford Univ, Dept Econ, Sequoia Hall, Stanford, CA 94305 USA

来源：

STATISTICA SINICA | 2022年 / 32卷 / 01期

关键词：

Data splitting; Hodges-Lehmann estimator; hypothesis testing; P-values; subsampling; U-statistics;

D O I：

10.5705/ss.202020.0048

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We present a general triangular array central limit theorem for U-statistics, where the kernel h(k) (x(1), ..., x(k)) and its dimension k may increase with the sample size. Motivating examples that require such a general result are presented, including a class of Hodges-Lehmann estimators, subsampling estimators, and combining p-values using data splitting. A result for the so-called M-statistic is also presented, which is defined as the median of some kernel computed over all subsets of the data of a given size. The conditions in the theorems are verified in the motivating examples as well.

引用

页码：323 / 344

页数：22

共 16 条

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