Intensity-based inference for planar point processes

B. Gail Ivanoff; Ely Merzbach

doi:10.1016/0047-259x(90)90085-v

Intensity-based inference for planar point processes

B. Gail Ivanoff
, Ely Merzbach

Department of Mathematics

University of Ottawa

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

The martingale methods of estimation are extended to point processes on the plane. A likelihood function is constructed and a general exponential formula is given. A central limit theorem is proved for processes which are both 1- and 2-martingales. Martingale estimators are defined, and consistency, sufficiency and asymptotic normality are discussed.

Original language	English
Pages (from-to)	269-281
Number of pages	13
Journal	Journal of Multivariate Analysis
Volume	32
Issue number	2
DOIs	https://doi.org/10.1016/0047-259x(90)90085-v
State	Published - Feb 1990

Bibliographical note

Funding Information:
Received April 13, 1989; revised August 28, 1989. Key words and phrases: planar point process, intensity-based inference, martingale, exponential formula, asymptotic normality. AMS 1980 subject classifications: primary 60655, 62AlO; secondary 60648, 6OG60. * Research supported by a grant from the Natural Sciences and Engineering Research Council of Canada. t Work done while the second author was visiting at the University of Ottawa. He wishes to thank the Department of Mathematics and especially Professor Ivanoff for their kind hospitality.

Funding

Received April 13, 1989; revised August 28, 1989. Key words and phrases: planar point process, intensity-based inference, martingale, exponential formula, asymptotic normality. AMS 1980 subject classifications: primary 60655, 62AlO; secondary 60648, 6OG60. * Research supported by a grant from the Natural Sciences and Engineering Research Council of Canada. t Work done while the second author was visiting at the University of Ottawa. He wishes to thank the Department of Mathematics and especially Professor Ivanoff for their kind hospitality.

Funders
Natural Sciences and Engineering Research Council of Canada

Keywords

asymptotic normality
exponential formula
intensity-based inference
martingale
planar point process

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10.1016/0047-259x(90)90085-v

Cite this

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AB - The martingale methods of estimation are extended to point processes on the plane. A likelihood function is constructed and a general exponential formula is given. A central limit theorem is proved for processes which are both 1- and 2-martingales. Martingale estimators are defined, and consistency, sufficiency and asymptotic normality are discussed.

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KW - intensity-based inference

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Intensity-based inference for planar point processes

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