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Activity Number:
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32
- Nonparametric Methods with High-Dimensional Data
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Type:
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Contributed
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Date/Time:
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Sunday, August 7, 2022 : 2:00 PM to 3:50 PM
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Sponsor:
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Section on Nonparametric Statistics
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Abstract #323259
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Title:
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Accuracy of the Bootstrap and the Normal Approximation in a High-Dimensional Framework
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Author(s):
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Mayya Zhilova*
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Companies:
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Georgia Institute of Technology
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Keywords:
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Edgeworth-type expansions;
Dependence on dimension;
Higher-order accuracy;
Bootstrapping;
Finite sample inference;
Berry–Esseen inequalities
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Abstract:
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In this talk we will address the problem of establishing a higher-order accuracy of bootstrapping procedures and (non-)normal approximation in a multivariate or high-dimensional setting. This topic is important for numerous problems in statistical inference and applications concerned with confidence estimation and hypothesis testing, and involving a growing dimension of an unknown parameter or high-dimensional random data. The new results outperform and/or refine accuracy of the normal approximation in existing Berry–Esseen inequalities under very general conditions. The established approximation bounds allow to track dependence of error terms on a dimension and a sample size in an explicit way. We also show optimality of these results in case of symmetrically distributed random summands. The talk will include an overview of statistical problems where the new results lead to improvements in accuracy of estimation procedures.
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Authors who are presenting talks have a * after their name.
