DeepAI AI Chat
Log In Sign Up

Point Process Regression

by   Álvaro Gajardo, et al.

Point processes in time have a wide range of applications that include the claims arrival process in insurance or the analysis of queues in operations research. Due to advances in technology, such samples of point processes are increasingly encountered. A key object of interest is the local intensity function. It has a straightforward interpretation that allows to understand and explore point process data. We consider functional approaches for point processes, where one has a sample of repeated realizations of the point process. This situation is inherently connected with Cox processes, where the intensity functions of the replications are modeled as random functions. Here we study a situation where one records covariates for each replication of the process, such as the daily temperature for bike rentals. For modeling point processes as responses with vector covariates as predictors we propose a novel regression approach for the intensity function that is intrinsically nonparametric. While the intensity function of a point process that is only observed once on a fixed domain cannot be identified, we show how covariates and repeated observations of the process can be utilized to make consistent estimation possible, and we also derive asymptotic rates of convergence without invoking parametric assumptions.


page 1

page 2

page 3

page 4


Spatial point processes intensity estimation with a diverging number of covariates

Feature selection procedures for spatial point processes parametric inte...

A Monad for Probabilistic Point Processes

A point process on a space is a random bag of elements of that space. In...

Multiresolution analysis of point processes and statistical thresholding for wavelet-based intensity estimation

We take a wavelet based approach to the analysis of point processes and ...

Testing For a Parametric Baseline-Intensity in Dynamic Interaction Networks

In statistical network analysis it is common to observe so called intera...

Analyzing the Spotify Top 200 Through a Point Process Lens

Every generation throws a hero up the pop charts. For the current genera...

PoPPy: A Point Process Toolbox Based on PyTorch

PoPPy is a Point Process toolbox based on PyTorch, which achieves flexib...