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A solution to a linear integral equation with an application to statistics of infinitely divisible moving averages
Author(s) -
Glück Jochen,
Roth Stefan,
Spodarev Evgeny
Publication year - 2022
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/sjos.12553
Subject(s) - mathematics , estimator , jump , uniqueness , measure (data warehouse) , integrator , mathematical analysis , function (biology) , nonparametric statistics , moving average , statistics , computer network , physics , bandwidth (computing) , quantum mechanics , database , evolutionary biology , computer science , biology
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 ) = ∫ℝ dg ( s ) w ( h ( s ) x ) d s , where g , h : ℝ d → ℝ are given measurable functions and v is a (weighted)L 2‐function on ℝ . We investigate conditions for the existence and uniqueness of this solution and giveL 2‐error bounds for the resulting estimates. An application to pure jump moving averages and a simulation study round off the paper.