Estimation of Poisson arrival processes under linear models

Autor:	Moore, Michael G., Davenport, Mark A.
Rok vydání:	2018
Předmět:	Computer Science - Information Theory Electrical Engineering and Systems Science - Signal Processing
Druh dokumentu:	Working Paper
Popis:	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.
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1803.00980 Zobrazit plný text záznamu View this record from Arxiv