Convolutional Splines for Regression Modeling With Point Process Valued Exposures

This is the authors' abstract. We don't add key points for this paper.

Point process valued exposure variables occur frequently in applied spatiotemporal statistics. However, existing statistical methods for incorporating these kinds of variables in regression analysis are limited. In particular, nonparametric modeling methods for working with these kinds of data are virtually nonexistent. In this article, we develop novel methods of non-parametrically representing point-process-valued covariates in spatiotemporal regression models and extend the representations to other types of complex spatial data. The novel methods can be used on their own for fully nonparametric regression or as extensions of existing parametric techniques. After developing the regression strategy, we provide efficient algorithms for estimating these models and illustrate the models via simulation and application to studying contributory sources of air pollution in western Pennsylvania.