Intensity-based inference for planar point processes

B. Gail Ivanoff, Ely Merzbach

Research output: Contribution to journalArticlepeer-review

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 languageEnglish
Pages (from-to)269-281
Number of pages13
JournalJournal of Multivariate Analysis
Volume32
Issue number2
DOIs
StatePublished - 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.

Keywords

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

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