ASYMPTOTICALLY INDEPENDENT U-STATISTICS IN HIGH-DIMENSIONAL TESTING.

Szczegóły
Abstrakt

Tytuł:: ASYMPTOTICALLY INDEPENDENT U-STATISTICS IN HIGH-DIMENSIONAL TESTING.
Autorzy:: He Y; Department of Statistics, University of Michigan.
Xu G; Department of Statistics, University of Michigan.
Wu C; Department of Statistics, Florida State University.
Pan W; Division of Biostatistics, School of Public Health, University of Minnesota.
Źródło:: Annals of statistics [Ann Stat] 2021 Feb; Vol. 49 (1), pp. 154-181. Date of Electronic Publication: 2021 Jan 29.
Typ publikacji:: Journal Article
Język:: English
Imprint Name(s):: Publication: Ithaca, NY : Project Euclid
Original Publication: San Francisco.
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Grant Information:: R01 GM113250 United States GM NIGMS NIH HHS; R01 GM126002 United States GM NIGMS NIH HHS; R01 HL105397 United States HL NHLBI NIH HHS; R01 HL116720 United States HL NHLBI NIH HHS
Contributed Indexing:: Keywords: 62F03; 62F05; High-dimensional hypothesis test; U-statistics; adaptive testing
Entry Date(s):: Date Created: 20211203 Latest Revision: 20240404
Update Code:: 20240404
PubMed Central ID:: PMC8634550
DOI:: 10.1214/20-aos1951
PMID:: 34857975
: Czasopismo naukowe

Many high-dimensional hypothesis tests aim to globally examine marginal or low-dimensional features of a high-dimensional joint distribution, such as testing of mean vectors, covariance matrices and regression coefficients. This paper constructs a family of U-statistics as unbiased estimators of the ℓ p -norms of those features. We show that under the null hypothesis, the U-statistics of different finite orders are asymptotically independent and normally distributed. Moreover, they are also asymptotically independent with the maximum-type test statistic, whose limiting distribution is an extreme value distribution. Based on the asymptotic independence property, we propose an adaptive testing procedure which combines p -values computed from the U-statistics of different orders. We further establish power analysis results and show that the proposed adaptive procedure maintains high power against various alternatives.

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