Model selection for Poisson processes with covariates

Details Model selection for Poisson processes with covariates Model selection for Poisson processes with covariates

2011-12-23

arxiv.org/abs/1112.5634v1

Mathematics

Statistics Theory

Scientific paper

We observe $n$ inhomogeneous Poisson processes with covariates and aim at estimating their intensities. To handle this problem, we assume that the intensity of each Poisson process is of the form $s (\cdot, x)$ where $x$ is the covariate and where $s$ is an unknown function. We propose a model selection approach where the models are used to approximate the multivariate function $s$. We show that our estimator satisfies an oracle-type inequality under very weak assumptions both on the intensities and the models. By using an Hellinger-type loss, we establish non-asymptotic risk bounds and specify them under various kind of assumptions on the target function $s$ such as being smooth or composite. Besides, we show that our estimation procedure is robust with respect to these assumptions.

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