2024
DOI: 10.5705/ss.202022.0354
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Asymptotic Independence of the Sum and Maximum of Dependent Random Variables with Applications to High-dimensional Tests

Abstract: For a set of dependent random variables, without stationary or the strong mixing assumptions, we derive the asymptotic independence between their sums and maxima. Then we apply this result to high-dimensional testing problems, where we combine the sum-type and max-type tests and propose a novel test procedure for the one-sample mean test, the two-sample mean test and the regression coefficient test in high-dimensional setting. Based on the asymptotic independence between sums and maxima, the asymptotic distrib… Show more

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