Statistical Properties of Point Process Learning for Gibbs Processes
Licentiatavhandling, 2024
In Paper 1 and 2, parameter estimation with PPL is done by minimizing loss functions, while Paper 3 explores an alternative approach to PPL, namely estimating equations. Further, statistical properties of the parameter estimator are derived in Paper 3, such as consistency and asymptotic normality for large samples, as well as bias and variance for small samples. It is concluded that the estimating equation approach is not feasible for PPL, whereby the original loss function-based approach is preferred. Moving on, Paper 3 then provides a theoretical foundation for the loss functions through an empirical risk formulation.
To conclude, PPL is shown to be a flexible and robust competitor to state-of-the-art methods for parameter estimation.
Gibbs processes
loss function
cross-validation
Takacs-Fiksel
pseudolikelihood
estimating equation
Papangelou conditional intensity
prediction error
thinning
point processes
Författare
Julia Jansson
Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik
Point Process Learning: a cross-validation-based statistical framework for point processes
Italian Statistical Society Series on Advances in Statistics,;Vol. 52(2025)
Paper i proceeding
Jansson, J., Cronie, O., Biscio C.A.N. Two perspectives on Point Process Learning: estimating equations and empirical risk minimisation. (2024) Manuscript.
Ämneskategorier
Sannolikhetsteori och statistik
Utgivare
Chalmers
Pascal, Hörsalsvägen 1
Opponent: Rasmus Waagepetersen