An estimator for Poisson means whose relative error distribution is known

2016/05/30 by Mark Huber, Huber, Mark
Mathematics · #62L12 #68W20 #Computation (stat.CO) #FOS: Computer and information sciences #msc:62L12 #msc:68W20 #stat.CO

paper · pdf · doi:10.48550/arxiv.1605.09445

10 pages, 1 table

arxiv created 2016/05/30 · arxiv updated 2016/06/01

Abstract

Suppose that X₁,X₂,… are a stream of independent, identically distributed Poisson random variables with mean μ. This work presents a new estimate μ_k for μ with the property that the distribution of the relative error in the estimate (( μ_k/μ) - 1) is known, and does not depend on μ in any way. This enables the construction of simple exact confidence intervals for the estimate, as well as a means of obtaining fast approximation algorithms for high dimensional integration using TPA. The new estimate requires a random number of Poisson draws, and so is best suited to Monte Carlo applications. As an example of such an application, the method is applied to obtain an exact confidence interval for the normalizing constant of the Ising model.

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