A Note on High-Dimensional Confidence Regions
Statistics Theory
2021-05-20 v1 Statistics Theory
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, -sparsely convex high-dimensional confidence regions are compared with respect to their volume. Specific confidence regions which are based on -balls are found to have exponentially smaller volume than the corresponding hypercube. The theoretical results are validated by a comprehensive simulation study.
Cite
@article{arxiv.2105.09028,
title = {A Note on High-Dimensional Confidence Regions},
author = {Sven Klaassen},
journal= {arXiv preprint arXiv:2105.09028},
year = {2021}
}
Comments
14 pages, 8 figures