Asymptotics of the Empirical Cross-over Function

Karthik Bharath; Vladimir Pozdnyakov; Dipak Dey

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arXiv · 1112.3427

Asymptotics of the Empirical Cross-over Function

Karthik Bharath·Vladimir Pozdnyakov·Dipak Dey

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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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Karthik Bharath, Vladimir Pozdnyakov, Dipak Dey. 2013-02-11. Asymptotics of the Empirical Cross-over Function. https://arxiv.org/abs/1112.3427

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