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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.

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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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R2 v1 2026-06-21T19:51:37.914Z