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In this work, based on a realization of an inhomogeneous Poisson processwhose intensity function depends on a real unknown parameter, we consider asimple hypothesis against a sequence of close (contiguous) alternatives. Undercertain regularity conditions we obtain the power loss of the score test withrespect to the Neyman-Pearson test. The power loss measures the performance ofa second order efficient test by the help of third order asymptotic propertiesof the problem under consideration.

Power Loss for Inhomogeneous Poisson Processes