Semi-parametric Inference for Regression Models Based on Marked Point Processes

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.