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• W2593270510 abstract "This paper is concerned with adaptive kernel estimation of the Lévy density $$N(x)$$ for bounded-variation pure-jump Lévy processes. The sample path is observed at $$n$$ discrete instants in the “high frequency” context ( $$Delta = Delta (n) $$ tends to zero while $$n Delta $$ tends to infinity). We construct a collection of kernel estimators of the function $$g(x)=xN(x)$$ and propose a method of local adaptive selection of the bandwidth. We provide an oracle inequality and a rate of convergence for the quadratic pointwise risk. This rate is proved to be the optimal minimax rate. We give examples and simulation results for processes fitting in our framework. We also consider the case of irregular sampling." @default.
• W2593270510 created "2017-03-16" @default.
• W2593270510 creator A5028462160 @default.
• W2593270510 creator A5039038830 @default.
• W2593270510 date "2015-01-10" @default.
• W2593270510 modified "2023-10-17" @default.
• W2593270510 title "Adaptive pointwise estimation for pure jump Lévy processes" @default.
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• W2593270510 doi "https://doi.org/10.1007/s11203-014-9113-6" @default.
• W2593270510 hasPublicationYear "2015" @default.
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