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 existing limit results. The law of large numbers, CLT and a functional CLT are proven.
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Bharath, K., Pozdnyakov, V. & Dey, D.K. Asymptotics of the Empirical Cross-over Function. Ann Inst Stat Math 66, 369–382 (2014). https://doi.org/10.1007/s10463-013-0423-z
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DOI: https://doi.org/10.1007/s10463-013-0423-z