Asymptotic Properties of Estimators for the Parameters of Spatial Inhomogeneous Poisson Point Processes

DOI10.2307/1427583zbMath0811.62090OpenAlexW2032072051MaRDI QIDQ4287973

Stephen L. Rathbun, Noel Cressie

Publication date: 4 May 1995

Published in: Advances in Applied Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/1427583

zbMATH Keywords

consistencyasymptotic normalityasymptotic efficiencymaximum likelihood estimatorspatial point processintensity functionBayesian estimatorlarge sample theoryinhomogeneous Poisson processeslinear combination of concomitant spatial variables

Mathematics Subject Classification ID

Asymptotic properties of parametric estimators (62F12) Inference from spatial processes (62M30) Asymptotic distribution theory in statistics (62E20) Geometric probability and stochastic geometry (60D05) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55)

Related Items (21)

A note on gaps in proofs of central limit theorems ⋮ Asymptotic properties of the maximum likelihood estimator for spatio-temporal point processes ⋮ What is the effective sample size of a spatial point process? ⋮ Variable selection using penalised likelihoods for point patterns on a linear network ⋮ Information criteria for inhomogeneous spatial point processes ⋮ Estimating abundance from counts in large data sets of irregularly spaced plots using spatial basis functions ⋮ Combining ungrouped and grouped wildfire data to estimate fire risk ⋮ Multivariate Temporal Point Process Regression ⋮ Spatial logistic regression and change-of-support in Poisson point processes ⋮ Point process modeling of wildfire hazard in Los Angeles county, California ⋮ Analytic computation of nonparametric Marsan–Lengliné estimates for Hawkes point processes ⋮ Mixed-Poisson point process with partially observed covariates: ecological momentary assessment of smoking ⋮ Estimation of the intensity of non-homogeneous point processes via wavelets ⋮ Variable selection for spatial Poisson point processes via a regularization method ⋮ Convex and non-convex regularization methods for spatial point processes intensity estimation ⋮ Leverage and Influence Diagnostics for Spatial Point Processes ⋮ Consistent parametric estimation of the intensity of a spatial-temporal point process ⋮ Score, pseudo-score and residual diagnostics for spatial point process models ⋮ Multiresolution analysis of point processes and statistical thresholding for Haar wavelet-based intensity estimation ⋮ Estimation of linear functionals of Poisson processes ⋮ Consistent estimation of the intensity function of a cyclic Poisson process.

This page was built for publication: Asymptotic Properties of Estimators for the Parameters of Spatial Inhomogeneous Poisson Point Processes