TY  - GEN
KW  - Lokale Likelihoods
KW  -  Statistische Netzwerkanalyse
N2  - In the present thesis we are interested in modelling the behaviour of actors in a network in dependence of explanatory variables which give information about every pair of actors. The behaviour is here expressed in interactions which the actors may cast amongst each other. Our model is based on a survival analysis idea: We assume that the interaction times between any two actors are encoded in a counting process such that we observe a counting process for any pair of actors. The intensity functions of these counting processes are then assumed to depend on the covariates in a certain parametric way. We allow that the parameters are time dependent functions, thereby the model becomes non-parametric. We present a rigorous analysis of the asymptotics of a non-parametric estimator based on a local likelihood approach. This includes point-wise asymptotics of the estimated parameter curves as well as asymptotics for an $L^2$-type test statistic.

In order to carry out the mathematical analysis of these terms we introduce three ideas to handle the complex dependence structure on the network. These provide different tools for handling covariances and proving concentration inequalities which might be of independent interest.

The theoretical analysis is complemented with an application to real-world data: We investigate the impact of different network quantities on a bike sharing network.
A1  - Kreiß, Alexander Günther
AV  - public
TI  - Local Maximum Likelihood Estimation of Time Dependent Parameters in Dynamic Interaction Networks
Y1  - 2019///
UR  - https://archiv.ub.uni-heidelberg.de/volltextserver/26395/
ID  - heidok26395
ER  -