Asymptotics of the Empirical Cross-over Function
Statistics Theory
2013-02-13 v4 Statistics Theory
Abstract
We consider a combination of heavily trimmed sums and sample quantiles which arises when examining properties of clustering criteria and prove limit theorems. The object of interest, which we call the Empirical Cross-over Function, is an L-statistic whose weights do not comply with the requisite regularity conditions for usage of ex- isting limit results. The law of large numbers, CLT and a functional CLT are proven.
Cite
@article{arxiv.1112.3427,
title = {Asymptotics of the Empirical Cross-over Function},
author = {Karthik Bharath and Vladimir Pozdnyakov and Dipak Dey},
journal= {arXiv preprint arXiv:1112.3427},
year = {2013}
}
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