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Luhm, A.; Pruscha, H. (1997): Semi-parametric Inference for Regression Models Based on Marked Point Processes. Sonderforschungsbereich 386, Discussion Paper 78
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Abstract

We study marked point processes (MPP's) with an arbitrary mark space. First we develop some statistically relevant topics in the theory of MPP's admitting an intensity kernel $\lambda_t(dz)$, namely martingale results, central limit theorems for both the number $n $ of objects under observation and the time $t $ tending to infinity, the decomposition into a local characteristic $(\lambda_t,\Phi_t(dz)) $ and a likelihood approach. Then we present semi-parametric statistical inference in a class of Aalen (1975)-type multiplicative regression models for MPP's as $n \to \infty$, using partial likelihood methods. Furthermore, considering the case $t \to \infty$, we study purely parametric M-estimators.