Probability Seminar: Liqian Zhang - Berry-Esseen bounds for U-statistics: Studentized and incomplete variants with applications to random forests
| Dates: | 7 May 2025 |
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| Times: | 15:00 - 16:00 |
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| What is it: | Seminar |
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| Organiser: | Department of Mathematics |
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Liqian Zhang (University of Manchester) will speak at the Probability seminar.
Title: Berry-Esseen bounds for U-statistics: Studentized and incomplete variants with applications to random forests
Keywords: Berry-Esseen bounds, asymptotic normality, Studentized non-linear statistics, Hoeffding decomposition, Stein’s method, incomplete U-statistics with Bernoulli sampling, honest random forests
Abstract: U-statistics are pivotal in statistical inference due to their symmetric nature as a functional algebraic generalization of an ordinary mean value. Establishing Berry-Esseen bounds for such statistics is crucial in quantifying the rate of convergence to normality. In practical hypothesis testing, the need to estimate variance gives rise to Studentized statistics, meanwhile the computational burden of high-order U-statistics calls for its incomplete versions. In this talk, we discuss Berry-Esseen bounds for these variants with the help of Stein’s method and Hoeffding decomposition. Finally, we explore how the theory of U-statistics can inform the choice of parameters in random forests — such as subsample size and number of trees — to attain the best convergence rate allowed by the data, especially in the context of honest forests used in causal inference.
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Frank Adams 2
Alan Turing Building
Manchester
