Nonuniform Berry-Esseen bounds for Studentized U-statistics

03/15/2023

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by   Dennis Leung, et al.

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We establish nonuniform Berry-Esseen (B-E) bounds for Studentized U-statistics of the rate 1/√(n) under a third-moment assumption, which covers the t-statistic that corresponds to a kernel of degree 1 as a special case. While an interesting data example raised by Novak (2005) can show that the form of the nonuniform bound for standardized U-statistics is actually invalid for their Studentized counterparts, our main results suggest that the validity of such a bound can be restored by minimally augmenting it with an additive term that decays exponentially in n. To our best knowledge, this is the first time that valid nonuniform B-E bounds for Studentized U-statistics have appeared in the literature.