Penalized maximum likelihood estimation for generalized linear point processes
Abstract
A generalized linear point process is specified in terms of an intensity that depends upon a linear predictor process through a fixed non-linear function. We present a framework where the linear predictor is parametrized by a Banach space and give results on Gateaux differentiability of the log-likelihood. Of particular interest is when the intensity is expressed in terms of a linear filter parametrized by a Sobolev space. Using that the Sobolev spaces are reproducing kernel Hilbert spaces we derive results on the representation of the penalized maximum likelihood estimator in a special case and the gradient of the negative log-likelihood in general. The latter is used to develop a descent algorithm in the Sobolev space. We conclude the paper by extensions to multivariate and additive model specifications. The methods are implemented in the R-package ppstat.
Cite
@article{arxiv.1003.0848,
title = {Penalized maximum likelihood estimation for generalized linear point processes},
author = {Niels Richard Hansen},
journal= {arXiv preprint arXiv:1003.0848},
year = {2013}
}