Estimation for nonhomogeneous Poisson processes from aggregated data

Authors:
Shane G. Henderson
Affiliations:
School of Operations Research and Industrial Engineering, Cornell University, 230 Rhodes Hall, Ithaca, NY 14853, USA
Venue:
Operations Research Letters
Year:
2003

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Abstract

A well-known heuristic for estimating the rate function or cumulative rate function of a nonhomogeneous Poisson process assumes that the rate function is piecewise constant on a set of data-independent intervals. We investigate the asymptotic (as the amount of data grows) behavior of this estimator in the case of equal interval widths, and show that it can be transformed into a consistent estimator if the interval lengths shrink at an appropriate rate as the amount of data grows.