Summary
Given independent, identically distributed copies of a mixed Poisson process N on a LCCB space E, i.e., a Cox process whose directing measure is of the form αm *, where α≧0 is a random variable with distribution σ and m * is a measure on E, we construct strongly consistent and asymptotically normal estimators of m * and the Laplace transform l σ. Methods are presented for estimating the directing measure of the (n+1)st process by combining the data for that process with estimates of appropriate quantities, the latter based on the first n processes. The case where different processes are observed over different sets is addressed.
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Research supported in part by the Air Force Office of Scientific Research, USAF, grant number AFOSR 82-0029. The United States Government is authorized to reproduce and distribute reprints for Governmental purposes
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Karr, A.F. Combined nonparametric inference and state estimation for mixed poisson processes. Z. Wahrscheinlichkeitstheorie verw Gebiete 66, 81–96 (1984). https://doi.org/10.1007/BF00532797
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DOI: https://doi.org/10.1007/BF00532797