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Mathematik, Informatik und Statistik - Open Access LMU - Teil 01/03 Podcast
Semi-parametric Inference for Regression Models Based on Marked Point Processes

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

Mathematik, Informatik und Statistik - Open Access LMU - Teil 01/03 vor 29 Jahren

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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.