Central Limit Theorems for Empirical Product Densities of Stationary Point Processes

  • We prove the asymptotic normality of kernel estimators of second- and higher-order product densities (and of the pair correlation function) for spatially homogeneous (and isotropic) point processes observed on a sampling window which is assumed to expand unboundedly in all directions. We first study the asymptotic behavior of the covariances of the empirical product densities under minimal moment and weak dependence assumptions. The proof of the main results is based on the Brillinger-mixing property of the underlying point process and certain smoothness conditions on the higher-order reduced cumulant measures. Finally, the obtained limit theorems allow to construct Chi-square-goodness-of-fit tests for hypothetical product densities.

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Author:Lothar HeinrichGND, Stella Klein
Frontdoor URLhttps://opus.bibliothek.uni-augsburg.de/opus4/1547
Series (Serial Number):Preprints des Instituts für Mathematik der Universität Augsburg (2011-10)
Publishing Institution:Universität Augsburg
Release Date:2011/07/19
Tag:Kernel-type product densities estimators; pair correlation function; Brillinger-mixing point processes; cumulant measures; large domain statistics
GND-Keyword:Räumliche Statistik; Zufälliger Punktprozess; Stationärer Punktprozess; Asymptotik; Anpassungstest; Zentraler Grenzwertsatz
Institutes:Mathematisch-Naturwissenschaftlich-Technische Fakultät
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik / Lehrstuhl für Stochastik und ihre Anwendungen
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Licence (German):Deutsches Urheberrecht