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- W2892362835 abstract "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 $ell_p$-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." @default.
- W2892362835 created "2018-09-27" @default.
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- W2892362835 date "2018-09-02" @default.
- W2892362835 modified "2023-09-26" @default.
- W2892362835 title "Asymptotically Independent U-Statistics in High-Dimensional Testing" @default.
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- W2892362835 doi "https://doi.org/10.48550/arxiv.1809.00411" @default.
- W2892362835 hasPublicationYear "2018" @default.
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