Penalized maximum likelihood estimation for generalized linear point processes

Niels Richard Hansen

Penalized maximum likelihood estimation for generalized linear point processes

Department of Mathematical Sciences

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.

Original language	English
Publication status	Published - 3 Mar 2010

Keywords

math.ST
math.PR
stat.ME
stat.TH

Cite this

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