Central Limit Theorem for the Integrated Squared Error of the Empirical Second-Order Product Density and Goodness-of-fit Tests for Stationary Point Processes
- Spatial point processes are mathematical models for irregular or random point patterns in the d-dimensional space, where usually d=2 or d=3 in applications. The second-order product density and its isotropic analogue, the pair correlation function, are important tools for analyzing stationary point processes. In the present work we derive central limit theorems for the integrated squared error (ISE) of the empirical second-order product density and for the ISE of the empirical pair correlation function for expanding observation windows. The proof techniques are based on higher-order cumulant measures and the Brillinger-mixing property of the underlying point processes. The obtained Gaussian limits are used for constructing asymptotic goodness-of-fit tests for checking point process hypotheses even in the non-Poissonian case.
| Author: | Stella Veronica David, Lothar HeinrichGND |
|---|---|
| URN: | urn:nbn:de:bvb:384-opus4-11890 |
| Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/1466 |
| Series (Serial Number): | Preprints des Instituts für Mathematik der Universität Augsburg (2010-17) |
| Type: | Preprint |
| Language: | English |
| Date of Publication (online): | 2010/12/06 |
| Year of first Publication: | 2010 |
| Publishing Institution: | Universität Augsburg |
| Release Date: | 2010/12/06 |
| Tag: | Brillinger-mixing; cumulant measures; model specification test; pair correlation function; second-order analysis of point processes |
| 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 |
