A solution to a linear integral equation with an application to statistics of infinitely divisible moving averages
| Autor: | Stefan Roth, Jochen Glück, Evgeny Spodarev |
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| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Statistics and Probability
Pure mathematics Measurable function Mathematics - Statistics Theory L2‐error bound Statistics Theory (math.ST) Measure (mathematics) Nonparametric signal detection moving average pure jump infinitely divisible random field Fourier transform on the multiplicative group ℝ∖{0} Moving average Inverse problems (Differential equations) FOS: Mathematics Inverses Problem Uniqueness ddc:510 nonparametric low‐frequency estimation Mathematics existence of unique solution Random field Estimator Lévy density Inverse problem Integral equation Lévy–Kchintchin representation DDC 510 / Mathematics linear integral equation Statistics Probability and Uncertainty |
| Popis: | 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. publishedVersion |
| Databáze: | OpenAIRE |
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