Single-index model for inhomogeneous spatial point processes

Yixin Fang, Ji Meng Loh

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

We introduce a single index model for the intensity of an inhomogeneous spatial point process, relating the intensity function to an unknown function p of a linear combination of measurements of a p-dimensional spatial covariate process. Such a model extends and generalizes a commonly used model where p is known. We derive an estimating procedure for p and the coefficient parameters β and show consistency and asymptotic normality of estimates of β under some regularity assumptions. We present results of some simulation studies showing the effectiveness of the procedure. Finally, we apply the procedure to a dataset of fast food restaurant locations in New York City.

Original languageEnglish (US)
Pages (from-to)555-574
Number of pages20
JournalStatistica Sinica
Volume27
Issue number2
DOIs
StatePublished - Apr 2017

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Keywords

  • Asymptotic normality
  • Consistency
  • Fast food restaurant data
  • Single-index model
  • Spatial point processes

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