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State estimation for cox processes with unknown probability law

Author

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  • Karr, Alan F.

Abstract

Let Ni, i[greater-or-equal, slanted]1, be i.i.d. observable Cox processes on a compact metric space E, directed by unobservable random measures Mi. Assume that the probability law of the Mi is completely unknown. Techniques are developed for approximation of state estimators using data from the processes N1,...,Nn to estimate necessary attributes of the unknown probability law of the time Mi. The techniques are based on representation of the state estimators in terms of reduced Palm distributions of the Ni and on estimation of these Palm distributions. Estimators of Palm distributions are shown to be strongly consistent and asymptotically normal. The difference between the true and the pseudo-state estimators converges to zero in L2 at rate n- for each [delta] > 0.

Suggested Citation

  • Karr, Alan F., 1985. "State estimation for cox processes with unknown probability law," Stochastic Processes and their Applications, Elsevier, vol. 20(1), pages 115-131, July.
    • Handle: RePEc:eee:spapps:v:20:y:1985:i:1:p:115-131
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