An inverse problem for infinitely divisible moving average random fields

Wolfgang Karcher, Stefan Roth, Evgeny Spodarev () and Corinna Walk
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Wolfgang Karcher: Ulm University
Stefan Roth: Ulm University
Evgeny Spodarev: Ulm University
Corinna Walk: Ulm University

Statistical Inference for Stochastic Processes, 2019, vol. 22, issue 2, No 4, 263-306

Abstract: Abstract Given a low frequency sample of an infinitely divisible moving average random field $$\{\int _{\mathbb {R}^d} f(x-t)\varLambda (dx); \ t \in \mathbb {R}^d \}$$ { ∫ R d f ( x - t ) Λ ( d x ) ; t ∈ R d } with a known simple function f, we study the problem of nonparametric estimation of the Lévy characteristics of the independently scattered random measure $$\varLambda $$ Λ . We provide three methods, a simple plug-in approach, a method based on Fourier transforms and an approach involving decompositions with respect to $$L^2$$ L 2 -orthonormal bases, which allow to estimate the Lévy density of $$\varLambda $$ Λ . For these methods, the bounds for the $$L^2$$ L 2 -error are given. Their numerical performance is compared in a simulation study.

Keywords: Infinitely divisible random measure; Stationary random field; Lévy process; Moving average; Lévy density; Fourier transform (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s11203-018-9188-6

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