Co-variance Operator of Banach Valued Random Elements: U-Statistic Approach
Statistics Theory
2023-11-20 v2 Probability
Statistics Theory
Abstract
This article proposes a co-variance operator for Banach valued random elements using the concept of -statistic. We then study the asymptotic distribution of the proposed co-variance operator along with related large sample properties. Moreover, specifically for Hilbert space valued random elements, the asymptotic distribution of the proposed estimator is derived even for dependent data under some mixing conditions.
Keywords
Cite
@article{arxiv.2307.03356,
title = {Co-variance Operator of Banach Valued Random Elements: U-Statistic Approach},
author = {Suprio Bhar and Subhra Sankar Dhar},
journal= {arXiv preprint arXiv:2307.03356},
year = {2023}
}
Comments
This revised version contains an updated literature review and an expanded appendix on some technical topics on Banach spaces