Asymptotic Palm likelihood theory for stationary point processes |
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Authors: | Michaela Prokešová Eva B Vedel Jensen |
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Institution: | 1. Department of Probability and Statistics, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75, Prague, Czech Republic 2. Department of Mathematics, Centre for Stochastic Geometry and Advanced Bioimaging, Aarhus University, Ny Munkegade 118, Building 1530, 8000, Aarhus C, Denmark
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Abstract: | In the present paper, we propose a Palm likelihood approach as a general estimating principle for stationary point processes in $\mathbf{R}^d$ for which the density of the second-order factorial moment measure is available in closed form or in an integral representation. Examples of such point processes include the Neyman–Scott processes and the log Gaussian Cox processes. The computations involved in determining the Palm likelihood estimator are simple. Conditions are provided under which the Palm likelihood estimator is strongly consistent and asymptotically normally distributed. |
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