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Two-step estimation procedures for inhomogeneous shot-noise Cox processes

By Michaela Prokesová, Jirí Dvorá and Eva B.V. Jensen
CSGB Research Reports
No. 02, February 2014

In the present paper we develop several two-step estimation procedures for inhomogeneous shot-noise Cox processes. The intensity function is parametrized by the inhomogeneity parameters while the pair-correlation function is parametrized by the interaction parameters. The suggested procedures are based on a combination of Poisson likelihood estimation of the inhomogeneity parameters in the first step and an adaptation of a method from the homogeneous case for estimation of the interaction parameters in the second step. The adapted methods, based on minimum contrast estimation, composite likelihood and Palm likelihood, are compared both theoretically and by means of a simulation study. Two-step estimation with Palm likelihood has not been considered before. Asymptotic normality of the two-step estimator with Palm likelihood is proved.

Keywords: Shot-noise Cox processes, Inhomogeneous spatial point processes, Two-step estimation methods, Palm likelihood, Asymptotic normality

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