A solution to a linear integral equation with an application to statistics of infinitely divisible moving averages

Jochen Glück, Stefan Roth and Evgeny Spodarev

Scandinavian Journal of Statistics, 2022, vol. 49, issue 3, 1244-1273

Abstract: For a stationary moving average random field, a nonparametric low frequency estimator of the Lévy density of its infinitely divisible independently scattered integrator measure is given. The plug‐in estimate is based on the solution w of the linear integral equation v(x)=∫ℝdg(s)w(h(s)x)ds, where g,h:ℝd→ℝ are given measurable functions and v is a (weighted) L2‐function on ℝ. We investigate conditions for the existence and uniqueness of this solution and give L2‐error bounds for the resulting estimates. An application to pure jump moving averages and a simulation study round off the paper.

Date: 2022
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