Estimating the Period of a Cyclic Non‐Homogeneous Poisson Process |
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Authors: | EDUARD BELITSER PAULO SERRA HARRY VAN ZANTEN |
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Institution: | Department of Mathematics, Eindhoven University of Technology |
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Abstract: | Abstract. Motivated by applications of Poisson processes for modelling periodic time‐varying phenomena, we study a semi‐parametric estimator of the period of cyclic intensity function of a non‐homogeneous Poisson process. There are no parametric assumptions on the intensity function which is treated as an infinite dimensional nuisance parameter. We propose a new family of estimators for the period of the intensity function, address the identifiability and consistency issues and present simulations which demonstrate good performance of the proposed estimation procedure in practice. We compare our method to competing methods on synthetic data and apply it to a real data set from a call center. |
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Keywords: | ergodic theorem identifiability m‐estimator non‐homogeneous poisson process periodic estimation period intensity semi‐parametric estimation |
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