Approximating symmetrized estimators of scatter via balanced incomplete U-statistics
Abstract
We derive limiting distributions of symmetrized estimators of scatter. Instead of considering all n(n−1)/2 pairs of the n observations, we only use nd suitably chosen pairs, where d≥1 is substantially smaller than n. It turns out that the resulting estimators are asymptotically equivalent to the original one whenever d=d(n)→∞ at arbitrarily slow speed. We also investigate the asymptotic properties for arbitrary fixed d. These considerations and numerical examples indicate that for practical purposes, moderate fixed values of d between 10 and 20 yield already estimators which are computationally feasible and rather close to the original ones.
Main Authors
Format
Articles
Research article
Published
2024
Series
Subjects
Publication in research information system
Publisher
Springer
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-202308254779Käytä tätä linkitykseen.
Review status
Peer reviewed
ISSN
0020-3157
DOI
https://doi.org/10.1007/s10463-023-00879-1
Language
English
Published in
Annals of the Institute of Statistical Mathematics
Citation
- Dümbgen, L., & Nordhausen, K. (2024). Approximating symmetrized estimators of scatter via balanced incomplete U-statistics. Annals of the Institute of Statistical Mathematics, 76(2), 185-207. https://doi.org/10.1007/s10463-023-00879-1
License
Copyright© The Institute of Statistical Mathematics, Tokyo 2023