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

摘要

For a stationary moving average random field, a nonparametric low frequency estimator of the Levy 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)=integral Double-struck capital Rdg(s)w(h(s)x)ds, where g,h:Double-struck capital Rd -> Double-struck capital R are given measurable functions and v is a (weighted) L2-function on Double-struck capital 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.