Central Limit Theorem for Mean and Variogram Estimators in Lévy–based Models

Anders Rønn-Nielsen, Eva B. Vedel Jensen

Research output: Working paperResearch

Abstract

We consider an infinitely divisible random field in Rd given as an integral of a
kernel function with respect to a Lévy basis. Under mild regularity conditions
we derive central limit theorems for the moment estimators of the mean and
the variogram of the field.
Original languageEnglish
Place of PublicationAarhus
PublisherCentre for Stochastic Geometry and Advanced Bioimaging (CSGB), Aarhus University
Number of pages16
Publication statusPublished - Jun 2018
SeriesCSGB Research Reports
Number06

Keywords

  • Central limit theorem
  • Infinite divisibility
  • Lévy-based modelling

Cite this

Rønn-Nielsen, A., & Jensen, E. B. V. (2018). Central Limit Theorem for Mean and Variogram Estimators in Lévy–based Models. Aarhus: Centre for Stochastic Geometry and Advanced Bioimaging (CSGB), Aarhus University. CSGB Research Reports, No. 06
Rønn-Nielsen, Anders ; Jensen, Eva B. Vedel. / Central Limit Theorem for Mean and Variogram Estimators in Lévy–based Models. Aarhus : Centre for Stochastic Geometry and Advanced Bioimaging (CSGB), Aarhus University, 2018. (CSGB Research Reports; No. 06).
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abstract = "We consider an infinitely divisible random field in Rd given as an integral of akernel function with respect to a L{\'e}vy basis. Under mild regularity conditionswe derive central limit theorems for the moment estimators of the mean andthe variogram of the field.",
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Rønn-Nielsen, A & Jensen, EBV 2018 'Central Limit Theorem for Mean and Variogram Estimators in Lévy–based Models' Centre for Stochastic Geometry and Advanced Bioimaging (CSGB), Aarhus University, Aarhus.

Central Limit Theorem for Mean and Variogram Estimators in Lévy–based Models. / Rønn-Nielsen, Anders ; Jensen, Eva B. Vedel.

Aarhus : Centre for Stochastic Geometry and Advanced Bioimaging (CSGB), Aarhus University, 2018.

Research output: Working paperResearch

TY - UNPB

T1 - Central Limit Theorem for Mean and Variogram Estimators in Lévy–based Models

AU - Rønn-Nielsen, Anders

AU - Jensen, Eva B. Vedel

PY - 2018/6

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AB - We consider an infinitely divisible random field in Rd given as an integral of akernel function with respect to a Lévy basis. Under mild regularity conditionswe derive central limit theorems for the moment estimators of the mean andthe variogram of the field.

KW - Central limit theorem

KW - Infinite divisibility

KW - Lévy-based modelling

KW - Central limit theorem

KW - Infinite divisibility

KW - Lévy-based modelling

M3 - Working paper

BT - Central Limit Theorem for Mean and Variogram Estimators in Lévy–based Models

PB - Centre for Stochastic Geometry and Advanced Bioimaging (CSGB), Aarhus University

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Rønn-Nielsen A, Jensen EBV. Central Limit Theorem for Mean and Variogram Estimators in Lévy–based Models. Aarhus: Centre for Stochastic Geometry and Advanced Bioimaging (CSGB), Aarhus University. 2018 Jun.