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Estimating the Period of a Cyclic Non‐Homogeneous Poisson Process
Author(s) -
BELITSER EDUARD,
SERRA PAULO,
ZANTEN HARRY VAN
Publication year - 2013
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/j.1467-9469.2012.00806.x
Subject(s) - mathematics , identifiability , consistency (knowledge bases) , estimator , poisson distribution , function (biology) , compound poisson process , statistics , parametric statistics , econometrics , poisson process , evolutionary biology , biology , geometry
. 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.