Asymptotics of the Empirical Cross-over Function
arXiv:1112.3427
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.
Submitted