Asymptotics of the Empirical Cross-over Function

2011/12/15 by Karthik Bharath, Bharath, Karthik, Vladimir Pozdnyakov +3
Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Financial Risk and Volatility Modeling #Statistical Methods and Inference #Statistics Theory (math.ST) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1112.3427

openalex publication_date 2011/12/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Testing for jumps in a discretely observed process

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