Estimation of Poisson arrival processes under linear models

Michael G. Moore; Mark A. Davenport

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arXiv · 1803.00980

Estimation of Poisson arrival processes under linear models

Michael G. Moore·Mark A. Davenport

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Abstract

In this paper we consider the problem of estimating the parameters of a Poisson arrival process where the rate function is assumed to lie in the span of a known basis. Our goal is to estimate the basis expansions coefficients given a realization of this process. We establish novel guarantees concerning the accuracy achieved by the maximum likelihood estimate. Our initial result is near-optimal, with the exception of an undesirable dependence on the dynamic range of the rate function. We then show how to remove this dependence through a process of "noise regularization", which results in an improved bound. We conjecture that a similar guarantee should be possible when using a more direct (deterministic) regularization scheme. We conclude with a discussion of practical applications and an empirical examination of the proposed regularization schemes.

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BibTeX RIS

Michael G. Moore, Mark A. Davenport. 2018-03-02. Estimation of Poisson arrival processes under linear models. https://arxiv.org/abs/1803.00980

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