An Inverse Problem for Infinitely Divisible Moving Average Random Fields

Wolfgang Karcher; Stefan Roth; Evgeny Spodarev; Corinna Walk

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arXiv · 1705.09542

An Inverse Problem for Infinitely Divisible Moving Average Random Fields

Wolfgang Karcher·Stefan Roth·Evgeny Spodarev·Corinna Walk

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Abstract

Given a low frequency sample of an infinitely divisible moving average random field $\{\int_{\mathbb{R}^d} f(x-t)\Lambda(dx); \ t \in \mathbb{R}^d \}$ with a known simple function $f$, we study the problem of nonparametric estimation of the L\'{e}vy characteristics of the independently scattered random measure $\Lambda$. We provide three methods, a simple plug-in approach, a method based on Fourier transforms and an approach involving decompositions with respect to $L^2$-orthonormal bases, which allow to estimate the L\'{e}vy density of $\Lambda$. For these methods, the bounds for the $L^2$-error are given. Their numerical performance is compared in a simulation study.

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BibTeX RIS

Wolfgang Karcher, Stefan Roth, Evgeny Spodarev, Corinna Walk. 2017-05-26. An Inverse Problem for Infinitely Divisible Moving Average Random Fields. https://arxiv.org/abs/1705.09542

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