Nonparametric intensity estimation from noisy observations of a Poisson process under unknown error distribution

Martin Kroll ()
Additional contact information
Martin Kroll: Universität Mannheim

Metrika: International Journal for Theoretical and Applied Statistics, 2019, vol. 82, issue 8, No 4, 990 pages

Abstract: Abstract We consider the nonparametric estimation of the intensity function of a Poisson point process in a circular model from indirect observations $$N_1,\ldots ,N_n$$ N 1 , … , N n . These observations emerge from hidden point process realizations with the target intensity through contamination with additive error. In case that the error distribution can only be estimated from an additional sample $$Y_1,\ldots ,Y_m$$ Y 1 , … , Y m we derive minimax rates of convergence with respect to the sample sizes n and m under abstract smoothness conditions and propose an orthonormal series estimator which attains the optimal rate of convergence. The performance of the estimator depends on the correct specification of a dimension parameter whose optimal choice relies on smoothness characteristics of both the intensity and the error density. We propose a data-driven choice of the dimension parameter based on model selection and show that the adaptive estimator attains the minimax optimal rate.

Keywords: Poisson point process; Intensity function; Statistical inverse problem; Adaptive estimation; Model selection (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1007/s00184-019-00716-7 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:metrik:v:82:y:2019:i:8:d:10.1007_s00184-019-00716-7

Ordering information: This journal article can be ordered from
http://www.springer.com/statistics/journal/184/PS2

DOI: 10.1007/s00184-019-00716-7

Access Statistics for this article

Metrika: International Journal for Theoretical and Applied Statistics is currently edited by U. Kamps and Norbert Henze

More articles in Metrika: International Journal for Theoretical and Applied Statistics from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().