Luhm, A.; Pruscha, H.
Semi-parametric Inference for Regression Models Based on Marked Point Processes.
Collaborative Research Center 386, Discussion Paper 78
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.