A Note on High-Dimensional Confidence Regions

Sven Klaassen

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arXiv · 2105.09028

A Note on High-Dimensional Confidence Regions

Sven Klaassen

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Abstract

Recent advances in statistics introduced versions of the central limit theorem for high-dimensional vectors, allowing for the construction of confidence regions for high-dimensional parameters. In this note, $s$-sparsely convex high-dimensional confidence regions are compared with respect to their volume. Specific confidence regions which are based on $\ell_p$-balls are found to have exponentially smaller volume than the corresponding hypercube. The theoretical results are validated by a comprehensive simulation study.

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Sven Klaassen. 2021-05-19. A Note on High-Dimensional Confidence Regions. https://arxiv.org/abs/2105.09028

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